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Uhol – Wikipédia

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class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Obsah</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">presunúť do postranného panelu</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">skryť</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Začiatok</div> </a> </li> <li id="toc-Pomenovania" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Pomenovania"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Pomenovania</span> </div> </a> <ul id="toc-Pomenovania-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Druhy_uhlov" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Druhy_uhlov"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Druhy uhlov</span> </div> </a> <ul id="toc-Druhy_uhlov-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dvojice_uhlov" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Dvojice_uhlov"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Dvojice uhlov</span> </div> </a> <ul id="toc-Dvojice_uhlov-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Súmernosť" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Súmernosť"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Súmernosť</span> </div> </a> <ul id="toc-Súmernosť-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Orientovaný_uhol" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Orientovaný_uhol"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Orientovaný uhol</span> </div> </a> <ul id="toc-Orientovaný_uhol-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Veľkosť_uhla" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Veľkosť_uhla"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Veľkosť uhla</span> </div> </a> <button aria-controls="toc-Veľkosť_uhla-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Přepnout podsekci Veľkosť uhla</span> </button> <ul id="toc-Veľkosť_uhla-sublist" class="vector-toc-list"> <li id="toc-Oblúková_(radiánová)_miera" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Oblúková_(radiánová)_miera"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Oblúková (radiánová) miera</span> </div> </a> <ul id="toc-Oblúková_(radiánová)_miera-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Stupňová_miera" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Stupňová_miera"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Stupňová miera</span> </div> </a> <ul id="toc-Stupňová_miera-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Stotinná_miera" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Stotinná_miera"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>Stotinná miera</span> </div> </a> <ul id="toc-Stotinná_miera-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Príklady" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Príklady"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.4</span> <span>Príklady</span> </div> </a> <ul id="toc-Príklady-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Veľkosť_orientovaného_uhla" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Veľkosť_orientovaného_uhla"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.5</span> <span>Veľkosť orientovaného uhla</span> </div> </a> <ul id="toc-Veľkosť_orientovaného_uhla-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Operácie_s_uhlami" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Operácie_s_uhlami"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Operácie s uhlami</span> </div> </a> <button aria-controls="toc-Operácie_s_uhlami-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Přepnout podsekci Operácie s uhlami</span> </button> <ul id="toc-Operácie_s_uhlami-sublist" class="vector-toc-list"> <li id="toc-Operácie_s_orientovanými_uhlami" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Operácie_s_orientovanými_uhlami"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Operácie s orientovanými uhlami</span> </div> </a> <ul id="toc-Operácie_s_orientovanými_uhlami-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Meracie_prístroje" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Meracie_prístroje"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Meracie prístroje</span> </div> </a> <ul id="toc-Meracie_prístroje-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pozri_aj" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Pozri_aj"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Pozri aj</span> </div> </a> <ul id="toc-Pozri_aj-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Iné_projekty" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Iné_projekty"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Iné projekty</span> </div> </a> <ul id="toc-Iné_projekty-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Externé_odkazy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Externé_odkazy"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Externé odkazy</span> </div> </a> <ul id="toc-Externé_odkazy-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Obsah" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Obsah" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Prepnúť obsah" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Prepnúť obsah</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Uhol</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Prejsť na článok v inom jazyku. Je dostupný v 140 jazykoch" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-140" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">140 jazykov</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Hoek_(meetkunde)" title="Hoek (meetkunde) – afrikánčina" lang="af" hreflang="af" data-title="Hoek (meetkunde)" data-language-autonym="Afrikaans" data-language-local-name="afrikánčina" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Winkel_(Geometrie)" title="Winkel (Geometrie) – nemčina (švajčiarska)" lang="gsw" hreflang="gsw" data-title="Winkel (Geometrie)" data-language-autonym="Alemannisch" data-language-local-name="nemčina (švajčiarska)" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Anglo" title="Anglo – aragónčina" lang="an" hreflang="an" data-title="Anglo" data-language-autonym="Aragonés" data-language-local-name="aragónčina" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B2%D8%A7%D9%88%D9%8A%D8%A9_(%D9%87%D9%86%D8%AF%D8%B3%D8%A9)" title="زاوية (هندسة) – arabčina" lang="ar" hreflang="ar" data-title="زاوية (هندسة)" data-language-autonym="العربية" data-language-local-name="arabčina" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-arc mw-list-item"><a href="https://arc.wikipedia.org/wiki/%DC%99%DC%98%DC%9D%DC%AC%DC%90_(%DC%A1%DC%9A%DC%AA%DC%98%DC%AC%DC%90)" title="ܙܘܝܬܐ (ܡܚܪܘܬܐ) – aramejčina" lang="arc" hreflang="arc" data-title="ܙܘܝܬܐ (ܡܚܪܘܬܐ)" data-language-autonym="ܐܪܡܝܐ" data-language-local-name="aramejčina" class="interlanguage-link-target"><span>ܐܪܡܝܐ</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D8%B2%D8%A7%D9%88%D9%8A%D8%A9" title="زاوية – arabština (marocká)" lang="ary" hreflang="ary" data-title="زاوية" data-language-autonym="الدارجة" data-language-local-name="arabština (marocká)" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%B2%D8%A7%D9%88%D9%8A%D9%87_(%D9%87%D9%86%D8%AF%D8%B3%D9%87)" title="زاويه (هندسه) – arabština (egyptská)" lang="arz" hreflang="arz" data-title="زاويه (هندسه)" data-language-autonym="مصرى" data-language-local-name="arabština (egyptská)" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%95%E0%A7%8B%E0%A6%A3" title="কোণ – ásamčina" lang="as" hreflang="as" data-title="কোণ" data-language-autonym="অসমীয়া" data-language-local-name="ásamčina" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/%C3%81ngulu" title="Ángulu – astúrčina" lang="ast" hreflang="ast" data-title="Ángulu" data-language-autonym="Asturianu" data-language-local-name="astúrčina" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-ay mw-list-item"><a href="https://ay.wikipedia.org/wiki/K%27uchu" title="K&#039;uchu – aymarčina" lang="ay" hreflang="ay" data-title="K&#039;uchu" data-language-autonym="Aymar aru" data-language-local-name="aymarčina" class="interlanguage-link-target"><span>Aymar aru</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Bucaq" title="Bucaq – azerbajdžančina" lang="az" hreflang="az" data-title="Bucaq" data-language-autonym="Azərbaycanca" data-language-local-name="azerbajdžančina" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%A2%DA%86%DB%8C" title="آچی – South Azerbaijani" lang="azb" hreflang="azb" data-title="آچی" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%9C%D3%A9%D0%B9%D3%A9%D1%88" title="Мөйөш – baškirčina" lang="ba" hreflang="ba" data-title="Мөйөш" data-language-autonym="Башҡортса" data-language-local-name="baškirčina" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Komps" title="Komps – žemaitština" lang="sgs" hreflang="sgs" data-title="Komps" data-language-autonym="Žemaitėška" data-language-local-name="žemaitština" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Anggulo" title="Anggulo – Central Bikol" lang="bcl" hreflang="bcl" data-title="Anggulo" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%92%D1%83%D0%B3%D0%B0%D0%BB" title="Вугал – bieloruština" lang="be" hreflang="be" data-title="Вугал" data-language-autonym="Беларуская" data-language-local-name="bieloruština" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9A%D1%83%D1%82" title="Кут – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Кут" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%AA%D0%B3%D1%8A%D0%BB" title="Ъгъл – bulharčina" lang="bg" hreflang="bg" data-title="Ъгъл" data-language-autonym="Български" data-language-local-name="bulharčina" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%95%E0%A7%8B%E0%A6%A3" title="কোণ – bengálčina" lang="bn" hreflang="bn" data-title="কোণ" data-language-autonym="বাংলা" data-language-local-name="bengálčina" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Korn_(mentoniezh)" title="Korn (mentoniezh) – bretónčina" lang="br" hreflang="br" data-title="Korn (mentoniezh)" data-language-autonym="Brezhoneg" data-language-local-name="bretónčina" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Ugao" title="Ugao – bosniačtina" lang="bs" hreflang="bs" data-title="Ugao" data-language-autonym="Bosanski" data-language-local-name="bosniačtina" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-bxr mw-list-item"><a href="https://bxr.wikipedia.org/wiki/%D2%AE%D0%BD%D1%81%D1%8D%D0%B3" title="Үнсэг – Russia Buriat" lang="bxr" hreflang="bxr" data-title="Үнсэг" data-language-autonym="Буряад" data-language-local-name="Russia Buriat" class="interlanguage-link-target"><span>Буряад</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Angle" title="Angle – katalánčina" lang="ca" hreflang="ca" data-title="Angle" data-language-autonym="Català" data-language-local-name="katalánčina" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-chr mw-list-item"><a href="https://chr.wikipedia.org/wiki/%E1%8E%A4%E1%8F%9C%E1%8F%85%E1%8F%9B_%E1%8E%A4%E1%8F%9E%E1%8F%B4%E1%8F%8D%E1%8F%9B" title="ᎤᏜᏅᏛ ᎤᏞᏴᏍᏛ – čerokí" lang="chr" hreflang="chr" data-title="ᎤᏜᏅᏛ ᎤᏞᏴᏍᏛ" data-language-autonym="ᏣᎳᎩ" data-language-local-name="čerokí" class="interlanguage-link-target"><span>ᏣᎳᎩ</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%AF%DB%86%D8%B4%DB%95" title="گۆشە – kurdčina (sorání)" lang="ckb" hreflang="ckb" data-title="گۆشە" data-language-autonym="کوردی" data-language-local-name="kurdčina (sorání)" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-crh mw-list-item"><a href="https://crh.wikipedia.org/wiki/Muyu%C5%9F" title="Muyuş – krymská tatárčina" lang="crh" hreflang="crh" data-title="Muyuş" data-language-autonym="Qırımtatarca" data-language-local-name="krymská tatárčina" class="interlanguage-link-target"><span>Qırımtatarca</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/%C3%9Ahel" title="Úhel – čeština" lang="cs" hreflang="cs" data-title="Úhel" data-language-autonym="Čeština" data-language-local-name="čeština" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cu mw-list-item"><a href="https://cu.wikipedia.org/wiki/%D1%AA%D0%B3%D1%8A%D0%BB%D1%8A" title="Ѫгълъ – cirkevná slovančina" lang="cu" hreflang="cu" data-title="Ѫгълъ" data-language-autonym="Словѣньскъ / ⰔⰎⰑⰂⰡⰐⰠⰔⰍⰟ" data-language-local-name="cirkevná slovančina" class="interlanguage-link-target"><span>Словѣньскъ / ⰔⰎⰑⰂⰡⰐⰠⰔⰍⰟ</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9A%C4%95%D1%82%D0%B5%D1%81" title="Кĕтес – čuvaština" lang="cv" hreflang="cv" data-title="Кĕтес" data-language-autonym="Чӑвашла" data-language-local-name="čuvaština" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Ongl" title="Ongl – waleština" lang="cy" hreflang="cy" data-title="Ongl" data-language-autonym="Cymraeg" data-language-local-name="waleština" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Vinkel" title="Vinkel – dánčina" lang="da" hreflang="da" data-title="Vinkel" data-language-autonym="Dansk" data-language-local-name="dánčina" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Winkel" title="Winkel – nemčina" lang="de" hreflang="de" data-title="Winkel" data-language-autonym="Deutsch" data-language-local-name="nemčina" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%93%CF%89%CE%BD%CE%AF%CE%B1" title="Γωνία – gréčtina" lang="el" hreflang="el" data-title="Γωνία" data-language-autonym="Ελληνικά" data-language-local-name="gréčtina" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Angle" title="Angle – angličtina" lang="en" hreflang="en" data-title="Angle" data-language-autonym="English" data-language-local-name="angličtina" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Angulo" title="Angulo – esperanto" lang="eo" hreflang="eo" data-title="Angulo" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/%C3%81ngulo" title="Ángulo – španielčina" lang="es" hreflang="es" data-title="Ángulo" data-language-autonym="Español" data-language-local-name="španielčina" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Nurk" title="Nurk – estónčina" lang="et" hreflang="et" data-title="Nurk" data-language-autonym="Eesti" data-language-local-name="estónčina" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Angelu_(geometria)" title="Angelu (geometria) – baskičtina" lang="eu" hreflang="eu" data-title="Angelu (geometria)" data-language-autonym="Euskara" data-language-local-name="baskičtina" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B2%D8%A7%D9%88%DB%8C%D9%87" title="زاویه – perzština" lang="fa" hreflang="fa" data-title="زاویه" data-language-autonym="فارسی" data-language-local-name="perzština" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Kulma" title="Kulma – fínčina" lang="fi" hreflang="fi" data-title="Kulma" data-language-autonym="Suomi" data-language-local-name="fínčina" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Tutuni" title="Tutuni – fidžijčina" lang="fj" hreflang="fj" data-title="Tutuni" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="fidžijčina" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Angle" title="Angle – francúzština" lang="fr" hreflang="fr" data-title="Angle" data-language-autonym="Français" data-language-local-name="francúzština" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Winkel" title="Winkel – severná frízština" lang="frr" hreflang="frr" data-title="Winkel" data-language-autonym="Nordfriisk" data-language-local-name="severná frízština" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Uillinn_(matamaitic)" title="Uillinn (matamaitic) – írčina" lang="ga" hreflang="ga" data-title="Uillinn (matamaitic)" data-language-autonym="Gaeilge" data-language-local-name="írčina" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E8%A7%92" title="角 – čínština (dialekty Gan)" lang="gan" hreflang="gan" data-title="角" data-language-autonym="贛語" data-language-local-name="čínština (dialekty Gan)" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Ang" title="Ang – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Ang" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Ce%C3%A0rn_(Matamataig)" title="Ceàrn (Matamataig) – škótska gaelčina" lang="gd" hreflang="gd" data-title="Ceàrn (Matamataig)" data-language-autonym="Gàidhlig" data-language-local-name="škótska gaelčina" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/%C3%81ngulo" title="Ángulo – galícijčina" lang="gl" hreflang="gl" data-title="Ángulo" data-language-autonym="Galego" data-language-local-name="galícijčina" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gn mw-list-item"><a href="https://gn.wikipedia.org/wiki/Takamby" title="Takamby – guaraníjčina" lang="gn" hreflang="gn" data-title="Takamby" data-language-autonym="Avañe&#039;ẽ" data-language-local-name="guaraníjčina" class="interlanguage-link-target"><span>Avañe&#039;ẽ</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%96%D7%95%D7%95%D7%99%D7%AA" title="זווית – hebrejčina" lang="he" hreflang="he" data-title="זווית" data-language-autonym="עברית" data-language-local-name="hebrejčina" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%95%E0%A5%8B%E0%A4%A3" title="कोण – hindčina" lang="hi" hreflang="hi" data-title="कोण" data-language-autonym="हिन्दी" data-language-local-name="hindčina" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Angle" title="Angle – hindština (Fidži)" lang="hif" hreflang="hif" data-title="Angle" data-language-autonym="Fiji Hindi" data-language-local-name="hindština (Fidži)" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Kut" title="Kut – chorvátčina" lang="hr" hreflang="hr" data-title="Kut" data-language-autonym="Hrvatski" data-language-local-name="chorvátčina" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Ang" title="Ang – haitská kreolčina" lang="ht" hreflang="ht" data-title="Ang" data-language-autonym="Kreyòl ayisyen" data-language-local-name="haitská kreolčina" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Sz%C3%B6g" title="Szög – maďarčina" lang="hu" hreflang="hu" data-title="Szög" data-language-autonym="Magyar" data-language-local-name="maďarčina" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B1%D5%B6%D5%AF%D5%B5%D5%B8%D6%82%D5%B6" title="Անկյուն – arménčina" lang="hy" hreflang="hy" data-title="Անկյուն" data-language-autonym="Հայերեն" data-language-local-name="arménčina" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hyw mw-list-item"><a href="https://hyw.wikipedia.org/wiki/%D4%B1%D5%B6%D5%AF%D5%AB%D6%82%D5%B6" title="Անկիւն – Western Armenian" lang="hyw" hreflang="hyw" data-title="Անկիւն" data-language-autonym="Արեւմտահայերէն" data-language-local-name="Western Armenian" class="interlanguage-link-target"><span>Արեւմտահայերէն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Angulo" title="Angulo – interlingua" lang="ia" hreflang="ia" data-title="Angulo" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Sudut_(geometri)" title="Sudut (geometri) – indonézština" lang="id" hreflang="id" data-title="Sudut (geometri)" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonézština" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ilo mw-list-item"><a href="https://ilo.wikipedia.org/wiki/Anggulo" title="Anggulo – ilokánčina" lang="ilo" hreflang="ilo" data-title="Anggulo" data-language-autonym="Ilokano" data-language-local-name="ilokánčina" class="interlanguage-link-target"><span>Ilokano</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Angulo" title="Angulo – ido" lang="io" hreflang="io" data-title="Angulo" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Horn_(r%C3%BAmfr%C3%A6%C3%B0i)" title="Horn (rúmfræði) – islandčina" lang="is" hreflang="is" data-title="Horn (rúmfræði)" data-language-autonym="Íslenska" data-language-local-name="islandčina" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Angolo" title="Angolo – taliančina" lang="it" hreflang="it" data-title="Angolo" data-language-autonym="Italiano" data-language-local-name="taliančina" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E8%A7%92%E5%BA%A6" title="角度 – japončina" lang="ja" hreflang="ja" data-title="角度" data-language-autonym="日本語" data-language-local-name="japončina" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Hanggl" title="Hanggl – jamajská kreolština" lang="jam" hreflang="jam" data-title="Hanggl" data-language-autonym="Patois" data-language-local-name="jamajská kreolština" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%99%E1%83%A3%E1%83%97%E1%83%AE%E1%83%94" title="კუთხე – gruzínčina" lang="ka" hreflang="ka" data-title="კუთხე" data-language-autonym="ქართული" data-language-local-name="gruzínčina" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kbd mw-list-item"><a href="https://kbd.wikipedia.org/wiki/%D0%9F%D0%BB%D3%80%D0%B0%D0%BD%D1%8D%D0%BF%D1%8D" title="ПлӀанэпэ – kabardčina" lang="kbd" hreflang="kbd" data-title="ПлӀанэпэ" data-language-autonym="Адыгэбзэ" data-language-local-name="kabardčina" class="interlanguage-link-target"><span>Адыгэбзэ</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%91%D2%B1%D1%80%D1%8B%D1%88_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F)" title="Бұрыш (геометрия) – kazaština" lang="kk" hreflang="kk" data-title="Бұрыш (геометрия)" data-language-autonym="Қазақша" data-language-local-name="kazaština" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%98%E1%9E%BB%E1%9F%86" title="មុំ – khmérčina" lang="km" hreflang="km" data-title="មុំ" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="khmérčina" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%95%E0%B3%8B%E0%B2%A8" title="ಕೋನ – kannadčina" lang="kn" hreflang="kn" data-title="ಕೋನ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="kannadčina" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B0%81_(%EC%88%98%ED%95%99)" title="각 (수학) – kórejčina" lang="ko" hreflang="ko" data-title="각 (수학)" data-language-autonym="한국어" data-language-local-name="kórejčina" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Hoke" title="Hoke – kurdčina" lang="ku" hreflang="ku" data-title="Hoke" data-language-autonym="Kurdî" data-language-local-name="kurdčina" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Angle" title="Angle – kornčina" lang="kw" hreflang="kw" data-title="Angle" data-language-autonym="Kernowek" data-language-local-name="kornčina" class="interlanguage-link-target"><span>Kernowek</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%91%D1%83%D1%80%D1%87" title="Бурч – kirgizština" lang="ky" hreflang="ky" data-title="Бурч" data-language-autonym="Кыргызча" data-language-local-name="kirgizština" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Angulus" title="Angulus – latinčina" lang="la" hreflang="la" data-title="Angulus" data-language-autonym="Latina" data-language-local-name="latinčina" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Hook" title="Hook – limburčina" lang="li" hreflang="li" data-title="Hook" data-language-autonym="Limburgs" data-language-local-name="limburčina" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Angol" title="Angol – lombardčina" lang="lmo" hreflang="lmo" data-title="Angol" data-language-autonym="Lombard" data-language-local-name="lombardčina" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-ln mw-list-item"><a href="https://ln.wikipedia.org/wiki/Lit%C3%BAmu" title="Litúmu – lingalčina" lang="ln" hreflang="ln" data-title="Litúmu" data-language-autonym="Lingála" data-language-local-name="lingalčina" class="interlanguage-link-target"><span>Lingála</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Kampas" title="Kampas – litovčina" lang="lt" hreflang="lt" data-title="Kampas" data-language-autonym="Lietuvių" data-language-local-name="litovčina" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Le%C5%86%C4%B7is" title="Leņķis – lotyština" lang="lv" hreflang="lv" data-title="Leņķis" data-language-autonym="Latviešu" data-language-local-name="lotyština" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mdf mw-list-item"><a href="https://mdf.wikipedia.org/wiki/%D0%A3%D0%B6%D0%B5%D1%81%D1%8C" title="Ужесь – mokšiančina" lang="mdf" hreflang="mdf" data-title="Ужесь" data-language-autonym="Мокшень" data-language-local-name="mokšiančina" class="interlanguage-link-target"><span>Мокшень</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Zoro_(je%C3%B4metria)" title="Zoro (jeômetria) – malgaština" lang="mg" hreflang="mg" data-title="Zoro (jeômetria)" data-language-autonym="Malagasy" data-language-local-name="malgaština" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mhr mw-list-item"><a href="https://mhr.wikipedia.org/wiki/%D0%9B%D1%83%D0%BA" title="Лук – Eastern Mari" lang="mhr" hreflang="mhr" data-title="Лук" data-language-autonym="Олык марий" data-language-local-name="Eastern Mari" class="interlanguage-link-target"><span>Олык марий</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%90%D0%B3%D0%BE%D0%BB" title="Агол – macedónčina" lang="mk" hreflang="mk" data-title="Агол" data-language-autonym="Македонски" data-language-local-name="macedónčina" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%95%E0%B5%8B%E0%B5%BA" title="കോൺ – malajálamčina" lang="ml" hreflang="ml" data-title="കോൺ" data-language-autonym="മലയാളം" data-language-local-name="malajálamčina" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D3%A8%D0%BD%D1%86%D3%A9%D0%B3_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80)" title="Өнцөг (геометр) – mongolčina" lang="mn" hreflang="mn" data-title="Өнцөг (геометр)" data-language-autonym="Монгол" data-language-local-name="mongolčina" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%95%E0%A5%8B%E0%A4%A8" title="कोन – maráthčina" lang="mr" hreflang="mr" data-title="कोन" data-language-autonym="मराठी" data-language-local-name="maráthčina" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Sudut" title="Sudut – malajčina" lang="ms" hreflang="ms" data-title="Sudut" data-language-autonym="Bahasa Melayu" data-language-local-name="malajčina" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%91%E1%80%B1%E1%80%AC%E1%80%84%E1%80%B7%E1%80%BA" title="ထောင့် – barmčina" lang="my" hreflang="my" data-title="ထောင့်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="barmčina" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-myv mw-list-item"><a href="https://myv.wikipedia.org/wiki/%D0%A3%D0%B6%D0%BE" title="Ужо – erzjančina" lang="myv" hreflang="myv" data-title="Ужо" data-language-autonym="Эрзянь" data-language-local-name="erzjančina" class="interlanguage-link-target"><span>Эрзянь</span></a></li><li class="interlanguage-link interwiki-mzn mw-list-item"><a href="https://mzn.wikipedia.org/wiki/%D8%B3%D9%88%DA%A9(%D9%87%D9%86%D9%91%D8%B3%D9%87)" title="سوک(هنّسه) – mázandaránčina" lang="mzn" hreflang="mzn" data-title="سوک(هنّسه)" data-language-autonym="مازِرونی" data-language-local-name="mázandaránčina" class="interlanguage-link-target"><span>مازِرونی</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Winkel_(Geometrie)" title="Winkel (Geometrie) – dolná nemčina" lang="nds" hreflang="nds" data-title="Winkel (Geometrie)" data-language-autonym="Plattdüütsch" data-language-local-name="dolná nemčina" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%95%E0%A5%8B%E0%A4%A3" title="कोण – nepálčina" lang="ne" hreflang="ne" data-title="कोण" data-language-autonym="नेपाली" data-language-local-name="nepálčina" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%95%E0%A5%81%E0%A4%82" title="कुं – nevárčina" lang="new" hreflang="new" data-title="कुं" data-language-autonym="नेपाल भाषा" data-language-local-name="nevárčina" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Hoek_(meetkunde)" title="Hoek (meetkunde) – holandčina" lang="nl" hreflang="nl" data-title="Hoek (meetkunde)" data-language-autonym="Nederlands" data-language-local-name="holandčina" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Vinkel" title="Vinkel – nórčina (nynorsk)" lang="nn" hreflang="nn" data-title="Vinkel" data-language-autonym="Norsk nynorsk" data-language-local-name="nórčina (nynorsk)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Vinkel" title="Vinkel – nórčina (bokmal)" lang="nb" hreflang="nb" data-title="Vinkel" data-language-autonym="Norsk bokmål" data-language-local-name="nórčina (bokmal)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nqo mw-list-item"><a href="https://nqo.wikipedia.org/wiki/%DF%9E%DF%8B%DF%B2%DF%9B%DF%90%DF%B2" title="ߞߋ߲ߛߐ߲ – n’ko" lang="nqo" hreflang="nqo" data-title="ߞߋ߲ߛߐ߲" data-language-autonym="ߒߞߏ" data-language-local-name="n’ko" class="interlanguage-link-target"><span>ߒߞߏ</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Angle" title="Angle – okcitánčina" lang="oc" hreflang="oc" data-title="Angle" data-language-autonym="Occitan" data-language-local-name="okcitánčina" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%95%E0%A9%8B%E0%A8%A8" title="ਕੋਨ – pandžábčina" lang="pa" hreflang="pa" data-title="ਕੋਨ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="pandžábčina" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/K%C4%85t" title="Kąt – poľština" lang="pl" hreflang="pl" data-title="Kąt" data-language-autonym="Polski" data-language-local-name="poľština" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%B2%D8%A7%D9%88%DB%8C%DB%81" title="زاویہ – Western Punjabi" lang="pnb" hreflang="pnb" data-title="زاویہ" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%B2%D8%A7%D9%88%D9%8A%D9%87" title="زاويه – paštčina" lang="ps" hreflang="ps" data-title="زاويه" data-language-autonym="پښتو" data-language-local-name="paštčina" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/%C3%82ngulo" title="Ângulo – portugalčina" lang="pt" hreflang="pt" data-title="Ângulo" data-language-autonym="Português" data-language-local-name="portugalčina" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Chhuka" title="Chhuka – kečuánčina" lang="qu" hreflang="qu" data-title="Chhuka" data-language-autonym="Runa Simi" data-language-local-name="kečuánčina" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Unghi" title="Unghi – rumunčina" lang="ro" hreflang="ro" data-title="Unghi" data-language-autonym="Română" data-language-local-name="rumunčina" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A3%D0%B3%D0%BE%D0%BB" title="Угол – ruština" lang="ru" hreflang="ru" data-title="Угол" data-language-autonym="Русский" data-language-local-name="ruština" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%9C%D1%83%D0%BD%D0%BD%D1%83%D0%BA" title="Муннук – jakutčina" lang="sah" hreflang="sah" data-title="Муннук" data-language-autonym="Саха тыла" data-language-local-name="jakutčina" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/%C3%80nculu" title="Ànculu – sicílčina" lang="scn" hreflang="scn" data-title="Ànculu" data-language-autonym="Sicilianu" data-language-local-name="sicílčina" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Ugao" title="Ugao – srbochorvátčina" lang="sh" hreflang="sh" data-title="Ugao" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="srbochorvátčina" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%9A%E0%B7%9D%E0%B6%AB%E0%B6%BA" title="කෝණය – sinhalčina" lang="si" hreflang="si" data-title="කෝණය" data-language-autonym="සිංහල" data-language-local-name="sinhalčina" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Angle" title="Angle – Simple English" lang="en-simple" hreflang="en-simple" data-title="Angle" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Kot" title="Kot – slovinčina" lang="sl" hreflang="sl" data-title="Kot" data-language-autonym="Slovenščina" data-language-local-name="slovinčina" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Gonyo" title="Gonyo – šončina" lang="sn" hreflang="sn" data-title="Gonyo" data-language-autonym="ChiShona" data-language-local-name="šončina" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Xagal" title="Xagal – somálčina" lang="so" hreflang="so" data-title="Xagal" data-language-autonym="Soomaaliga" data-language-local-name="somálčina" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/K%C3%ABndi" title="Këndi – albánčina" lang="sq" hreflang="sq" data-title="Këndi" data-language-autonym="Shqip" data-language-local-name="albánčina" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A3%D0%B3%D0%B0%D0%BE" title="Угао – srbčina" lang="sr" hreflang="sr" data-title="Угао" data-language-autonym="Српски / srpski" data-language-local-name="srbčina" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Juru_(%C3%A9lmu_ukur)" title="Juru (élmu ukur) – sundčina" lang="su" hreflang="su" data-title="Juru (élmu ukur)" data-language-autonym="Sunda" data-language-local-name="sundčina" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Vinkel" title="Vinkel – švédčina" lang="sv" hreflang="sv" data-title="Vinkel" data-language-autonym="Svenska" data-language-local-name="švédčina" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Pembe_(jiometria)" title="Pembe (jiometria) – swahilčina" lang="sw" hreflang="sw" data-title="Pembe (jiometria)" data-language-autonym="Kiswahili" data-language-local-name="swahilčina" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%95%E0%AF%8B%E0%AE%A3%E0%AE%AE%E0%AF%8D" title="கோணம் – tamilčina" lang="ta" hreflang="ta" data-title="கோணம்" data-language-autonym="தமிழ்" data-language-local-name="tamilčina" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%95%E0%B1%8B%E0%B0%A3%E0%B0%82" title="కోణం – telugčina" lang="te" hreflang="te" data-title="కోణం" data-language-autonym="తెలుగు" data-language-local-name="telugčina" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%9A%D1%83%D0%BD%D2%B7" title="Кунҷ – tadžičtina" lang="tg" hreflang="tg" data-title="Кунҷ" data-language-autonym="Тоҷикӣ" data-language-local-name="tadžičtina" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A1%E0%B8%B8%E0%B8%A1" title="มุม – thajčina" lang="th" hreflang="th" data-title="มุม" data-language-autonym="ไทย" data-language-local-name="thajčina" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Anggulo" title="Anggulo – tagalčina" lang="tl" hreflang="tl" data-title="Anggulo" data-language-autonym="Tagalog" data-language-local-name="tagalčina" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/A%C3%A7%C4%B1" title="Açı – turečtina" lang="tr" hreflang="tr" data-title="Açı" data-language-autonym="Türkçe" data-language-local-name="turečtina" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%9F%D0%BE%D1%87%D0%BC%D0%B0%D0%BA" title="Почмак – tatárčina" lang="tt" hreflang="tt" data-title="Почмак" data-language-autonym="Татарча / tatarça" data-language-local-name="tatárčina" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9A%D1%83%D1%82" title="Кут – ukrajinčina" lang="uk" hreflang="uk" data-title="Кут" data-language-autonym="Українська" data-language-local-name="ukrajinčina" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%B2%D8%A7%D9%88%DB%8C%DB%81" title="زاویہ – urdčina" lang="ur" hreflang="ur" data-title="زاویہ" data-language-autonym="اردو" data-language-local-name="urdčina" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Burchak" title="Burchak – uzbečtina" lang="uz" hreflang="uz" data-title="Burchak" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbečtina" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/G%C3%B3c" title="Góc – vietnamčina" lang="vi" hreflang="vi" data-title="Góc" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamčina" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Anggulo" title="Anggulo – waray" lang="war" hreflang="war" data-title="Anggulo" data-language-autonym="Winaray" data-language-local-name="waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E8%A7%92" title="角 – čínština (wu)" lang="wuu" hreflang="wuu" data-title="角" data-language-autonym="吴语" data-language-local-name="čínština (wu)" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%99%E1%83%A3%E1%83%9C%E1%83%97%E1%83%AE%E1%83%A3" title="კუნთხუ – mingrelština" lang="xmf" hreflang="xmf" data-title="კუნთხუ" data-language-autonym="მარგალური" data-language-local-name="mingrelština" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%95%D7%95%D7%99%D7%A0%D7%A7%D7%9C" title="ווינקל – jidiš" lang="yi" hreflang="yi" data-title="ווינקל" data-language-autonym="ייִדיש" data-language-local-name="jidiš" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%A7%92" title="角 – čínština" lang="zh" hreflang="zh" data-title="角" data-language-autonym="中文" data-language-local-name="čínština" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E8%A7%92" title="角 – čínština (klasická)" lang="lzh" hreflang="lzh" data-title="角" data-language-autonym="文言" data-language-local-name="čínština (klasická)" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Kak-t%C5%8D%CD%98" title="Kak-tō͘ – čínština (dialekty Minnan)" lang="nan" hreflang="nan" data-title="Kak-tō͘" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="čínština (dialekty Minnan)" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E8%A7%92_(%E5%B9%BE%E4%BD%95)" title="角 (幾何) – kantončina" lang="yue" hreflang="yue" data-title="角 (幾何)" data-language-autonym="粵語" data-language-local-name="kantončina" 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data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Vzhľad</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">presunúť do postranného panelu</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">skryť</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">z Wikipédie, slobodnej encyklopédie</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="sk" dir="ltr"><div style="background-color: #f9f9f9; border-bottom: 1px solid #aaaaaa; padding: 0.3em; margin-bottom: 0.5em;"><span typeof="mw:File"><a href="/wiki/S%C3%BAbor:Disambig.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Disambig.svg/17px-Disambig.svg.png" decoding="async" width="17" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Disambig.svg/26px-Disambig.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/72/Disambig.svg/34px-Disambig.svg.png 2x" data-file-width="230" data-file-height="183" /></a></span> O priestorovom uhle pozri <i><a href="/wiki/Priestorov%C3%BD_uhol" title="Priestorový uhol">priestorový uhol</a>.</i></div> <p><b>Uhol</b> alebo <b>rovinný uhol</b> je časť <a href="/wiki/Rovina_(geometria)" title="Rovina (geometria)">roviny</a> určený dvoma <a href="/wiki/Polpriamka" title="Polpriamka">polpriamkami</a> so spoločným začiatkom. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Pomenovania">Pomenovania</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Uhol&amp;veaction=edit&amp;section=1" title="Upraviť sekciu: Pomenovania" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Uhol&amp;action=edit&amp;section=1" title="Editovat zdrojový kód sekce Pomenovania"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File"><a href="/wiki/S%C3%BAbor:Uhol01_SK.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Uhol01_SK.jpg/150px-Uhol01_SK.jpg" decoding="async" width="150" height="159" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Uhol01_SK.jpg/225px-Uhol01_SK.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Uhol01_SK.jpg/300px-Uhol01_SK.jpg 2x" data-file-width="339" data-file-height="359" /></a><figcaption></figcaption></figure> <p>Polpriamky určujúce uhol v rovine sa volajú <i>ramená uhla</i>, spoločný bod ramien sa volá <i>vrchol uhla</i>. <a href="/wiki/Mno%C5%BEina" title="Množina">Množina</a> bodov roviny vyseknutej uhlom sa nazýva <i>vnútorné body uhla</i> (vnútrajšok uhla), ostatné body z roviny voláme <i>vonkajšie body uhla</i> (vonkajšok uhla). Uhol sa znázorňuje pomocou ramien, medzi ktorými sa vyznačí oblúčikom vrchol uhla. Zápis vnútorného uhla sa vykonáva pomocou písmen gréckej abecedy napr. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x3b1;<!-- α --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }" /></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x3b2;<!-- β --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }" /></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gamma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x3b3;<!-- γ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a223c880b0ce3da8f64ee33c4f0010beee400b1a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.262ex; height:2.176ex;" alt="{\displaystyle \gamma }" /></span>, vonkajší uhol sa označuje znakom vnútorného uhla s čiarkou <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x3b1;<!-- α --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }" /></span>', <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x3b2;<!-- β --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }" /></span>', <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gamma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x3b3;<!-- γ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a223c880b0ce3da8f64ee33c4f0010beee400b1a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.262ex; height:2.176ex;" alt="{\displaystyle \gamma }" /></span>'. Iným spôsobom označovania je pomocou symbolu uhla a troch bodov v poradí bod ramena&#160;–&#160;vrchol&#160;–&#160;bod na druhom ramene, napr. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \angle AVB}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">&#x2220;<!-- ∠ --></mi> <mi>A</mi> <mi>V</mi> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \angle AVB}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57fb19956aae83e7e94dade7234e58b1189f8445" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.972ex; height:2.176ex;" alt="{\displaystyle \angle AVB}" /></span>. </p> <div style="clear:both;"></div> <div class="mw-heading mw-heading2"><h2 id="Druhy_uhlov">Druhy uhlov</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Uhol&amp;veaction=edit&amp;section=2" title="Upraviť sekciu: Druhy uhlov" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Uhol&amp;action=edit&amp;section=2" title="Editovat zdrojový kód sekce Druhy uhlov"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><b>Nulový uhol</b> je uhol, ktorého ramená ležia na sebe (všetky ich body sú totožné). Má presne 0°.</li> <li><b>Ostrý uhol</b> je uhol menší ako pravý uhol. Má viac ako 0° ale menej ako 90°.</li> <li><b>Pravý uhol</b> je polovica priameho uhla. Označujeme ho bodkou v oblúčiku, alebo hranatým "oblúčikom". Má presne 90°.</li> <li><b>Tupý uhol</b> je väčší ako pravý uhol. Má viac ako 90° ale menej ako 180°.</li> <li><b>Priamy uhol</b> je uhol, ktorého ramená sú navzájom opačné polpriamky, čiže spolu vytvárajú priamku. Má presne 180°.</li> <li><b>Plný uhol</b> je uhol, ktorého ramená sú totožné (ležia na sebe). Za uhol považujeme celú rovinu okolo nich. Je to doplnok nulového uhla v rovine. Má presne 360°.</li> <li><b>Kosý uhol</b> je uhol, ktorý nie je nulový, pravý, priamy ani plný (šikmý, nepriamy, nerovnobežný).</li> <li><b>Dutý uhol</b> je uhol, ktorý je menší ako priamy.</li></ul> <p><span class="mw-default-size" typeof="mw:File"><a href="/wiki/S%C3%BAbor:DruhyUhluSK.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/9/98/DruhyUhluSK.jpg" decoding="async" width="579" height="108" class="mw-file-element" data-file-width="579" data-file-height="108" /></a></span> </p> <ul><li><b>Konvexný uhol</b> je uhol priamy, alebo menší než priamy</li> <li><b>Konkávny uhol</b> je väčší než priamy</li></ul> <div class="mw-heading mw-heading2"><h2 id="Dvojice_uhlov">Dvojice uhlov</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Uhol&amp;veaction=edit&amp;section=3" title="Upraviť sekciu: Dvojice uhlov" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Uhol&amp;action=edit&amp;section=3" title="Editovat zdrojový kód sekce Dvojice uhlov"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><b>Vrcholové uhly</b> sú dva uhly, ktorých ramená sú opačné polpriamky. Vrcholové uhly sú <a href="/wiki/Zhodnos%C5%A5" class="mw-disambig" title="Zhodnosť">zhodné</a>.</li></ul> <p><span class="mw-default-size" typeof="mw:File"><a href="/wiki/S%C3%BAbor:VrcholoveUhlySK.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/8/89/VrcholoveUhlySK.jpg" decoding="async" width="202" height="122" class="mw-file-element" data-file-width="202" data-file-height="122" /></a></span> </p> <ul><li><b>Vedľajšie (susedné) uhly</b> sú dva uhly, ktorých jedno rameno je spoločné a druhé ramená sú opačné polpriamky. Súčet vedľajších uhlov je priamy uhol, teda dva susedné uhly zvierajú 180°.</li></ul> <p><span class="mw-default-size" typeof="mw:File"><a href="/wiki/S%C3%BAbor:VedlejsiUhlySK.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/4/40/VedlejsiUhlySK.jpg" decoding="async" width="181" height="107" class="mw-file-element" data-file-width="181" data-file-height="107" /></a></span> </p> <ul><li><b>Súhlasné uhly</b> sú dva uhly, ktorých prvé ramená ležia na jednej <a href="/wiki/Priamka" title="Priamka">priamke</a> a druhé ramená sú rovnobežné, pritom smer príslušných ramien je rovnaký (súhlasný). Súhlasné uhly sú <i>zhodné</i>.</li></ul> <p><span class="mw-default-size" typeof="mw:File"><a href="/wiki/S%C3%BAbor:SouhlasneUhlySK.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/b/b8/SouhlasneUhlySK.jpg" decoding="async" width="188" height="139" class="mw-file-element" data-file-width="188" data-file-height="139" /></a></span> </p> <ul><li><b>Striedavé uhly</b> sú dva uhly, ktorých prvé ramená ležia na jednej priamke a druhé ramená sú rovnobežné, pritom smer príslušných ramien je opačný (striedavý). Striedavé uhly sú <i>zhodné</i>.</li></ul> <p><span class="mw-default-size" typeof="mw:File"><a href="/wiki/S%C3%BAbor:StridaveUhlySK.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/b/b5/StridaveUhlySK.jpg" decoding="async" width="193" height="139" class="mw-file-element" data-file-width="193" data-file-height="139" /></a></span> </p> <div class="mw-heading mw-heading2"><h2 id="Súmernosť"><span id="S.C3.BAmernos.C5.A5"></span>Súmernosť</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Uhol&amp;veaction=edit&amp;section=4" title="Upraviť sekciu: Súmernosť" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Uhol&amp;action=edit&amp;section=4" title="Editovat zdrojový kód sekce Súmernosť"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Všetky uhly sú <a href="/wiki/Osov%C3%A1_s%C3%BAmernos%C5%A5" title="Osová súmernosť">osovo súmerné</a>, os uhla prechádza vrcholom a rozdeľuje uhol na dve zhodné časti (polovice uhla). </p><p><span typeof="mw:File"><a href="/wiki/S%C3%BAbor:OsaUhluSK.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/OsaUhluSK.jpg/150px-OsaUhluSK.jpg" decoding="async" width="150" height="139" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/OsaUhluSK.jpg/225px-OsaUhluSK.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c8/OsaUhluSK.jpg/300px-OsaUhluSK.jpg 2x" data-file-width="329" data-file-height="305" /></a></span> </p> <div class="mw-heading mw-heading2"><h2 id="Orientovaný_uhol"><span id="Orientovan.C3.BD_uhol"></span>Orientovaný uhol</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Uhol&amp;veaction=edit&amp;section=5" title="Upraviť sekciu: Orientovaný uhol" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Uhol&amp;action=edit&amp;section=5" title="Editovat zdrojový kód sekce Orientovaný uhol"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Orientovaným uhlom nazývame <a href="/w/index.php?title=Usporiadan%C3%A9_n-tice&amp;action=edit&amp;redlink=1" class="new" title="Usporiadané n-tice (stránka neexistuje)">usporiadanú dvojicu</a> polpriamok <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {VA}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>V</mi> <mi>A</mi> </mrow> <mo stretchy="false">&#x2192;<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {VA}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/55153805638ff673fcd8a3b86b98f14513c0c0ef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.53ex; height:3.676ex;" alt="{\displaystyle {\vec {VA}}}" /></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {VB}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>V</mi> <mi>B</mi> </mrow> <mo stretchy="false">&#x2192;<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {VB}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5bac7f2471d3171569259ae6211d298dcac2c8bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.551ex; height:3.676ex;" alt="{\displaystyle {\vec {VB}}}" /></span> so spoločným bodom <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}" /></span>, pričom polpriamku <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {VA}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>V</mi> <mi>A</mi> </mrow> <mo stretchy="false">&#x2192;<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {VA}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/55153805638ff673fcd8a3b86b98f14513c0c0ef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.53ex; height:3.676ex;" alt="{\displaystyle {\vec {VA}}}" /></span> nazveme <i>počiatočným ramenom uhla</i> a polpriamku <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {VB}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>V</mi> <mi>B</mi> </mrow> <mo stretchy="false">&#x2192;<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {VB}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5bac7f2471d3171569259ae6211d298dcac2c8bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.551ex; height:3.676ex;" alt="{\displaystyle {\vec {VB}}}" /></span> nazveme <i>koncovým ramenom uhla</i>. Bod <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}" /></span> je vrcholom orientovaného uhla. </p> <div class="mw-heading mw-heading2"><h2 id="Veľkosť_uhla"><span id="Ve.C4.BEkos.C5.A5_uhla"></span>Veľkosť uhla</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Uhol&amp;veaction=edit&amp;section=6" title="Upraviť sekciu: Veľkosť uhla" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Uhol&amp;action=edit&amp;section=6" title="Editovat zdrojový kód sekce Veľkosť uhla"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Veľkosť uhla je nezáporné <a href="/wiki/%C4%8C%C3%ADslo" class="mw-disambig" title="Číslo">číslo</a>, ktoré sa dá priradiť každému uhlu. Platí pritom, že <a href="/wiki/Zhodnos%C5%A5" class="mw-disambig" title="Zhodnosť">zhodné</a> uhly majú rovnakú veľkosť a tiež, že <a href="/wiki/S%C3%BA%C4%8Det" class="mw-redirect" title="Súčet">súčet</a> veľkostí uhlov <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \angle AVX}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">&#x2220;<!-- ∠ --></mi> <mi>A</mi> <mi>V</mi> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \angle AVX}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29cbf7aac2affa96aaacef21a79bafbd56245a6d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.188ex; height:2.176ex;" alt="{\displaystyle \angle AVX}" /></span> a <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \angle XVB}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">&#x2220;<!-- ∠ --></mi> <mi>X</mi> <mi>V</mi> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \angle XVB}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c8402c1271bffbd24d277f8b644ae68b3b7ecc5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.209ex; height:2.176ex;" alt="{\displaystyle \angle XVB}" /></span> je rovný veľkosti uhla <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \angle AVB}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">&#x2220;<!-- ∠ --></mi> <mi>A</mi> <mi>V</mi> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \angle AVB}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57fb19956aae83e7e94dade7234e58b1189f8445" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.972ex; height:2.176ex;" alt="{\displaystyle \angle AVB}" /></span>. </p><p>Číselná veľkosť uhla je daná voľbou nenulového uhla, ktorému priradíme veľkosť 1. V praxi sa pre meranie uhla používa </p> <div class="mw-heading mw-heading3"><h3 id="Oblúková_(radiánová)_miera"><span id="Obl.C3.BAkov.C3.A1_.28radi.C3.A1nov.C3.A1.29_miera"></span>Oblúková (radiánová) miera</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Uhol&amp;veaction=edit&amp;section=7" title="Upraviť sekciu: Oblúková (radiánová) miera" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Uhol&amp;action=edit&amp;section=7" title="Editovat zdrojový kód sekce Oblúková (radiánová) miera"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Hodnota jednotkového uhla v oblúkovej miere je zvolená tak, že uhol o veľkosti 1 vymedzuje na <a href="/wiki/Kru%C5%BEnica" title="Kružnica">kružnici</a> so stredom vo vrchole uhla <a href="/wiki/Obl%C3%BAk" title="Oblúk">oblúk</a>, ktorého dĺžka je rovná <a href="/wiki/Polomer" class="mw-disambig" title="Polomer">polomeru</a> danej kružnice. Hodnotu oblúkovej miery uhla <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x3b1;<!-- α --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }" /></span> značíme <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {arc} \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>arc</mi> <mo>&#x2061;<!-- ⁡ --></mo> <mi>&#x3b1;<!-- α --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {arc} \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bff68da407ac5136ef779bf361aaa048603d94b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.981ex; height:1.676ex;" alt="{\displaystyle \operatorname {arc} \alpha }" /></span>. </p><p>Veľkosť ľubovoľného uhla je možné určiť ako pomer dĺžky oblúka vymedzeného ramenami na kružnici opísanej okolo vrcholu k polomeru tejto kružnice, tzn. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha ={\frac {s}{r}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x3b1;<!-- α --></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>s</mi> <mi>r</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha ={\frac {s}{r}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b357d59c75795f0c34835df0b78c2e58c0e18ef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:6.513ex; height:4.676ex;" alt="{\displaystyle \alpha ={\frac {s}{r}}}" /></span>,</dd></dl> <p>kde <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}" /></span> je dĺžka kruhového oblúka medzi priamkami, ktoré vymedzujú uhol, a <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}" /></span> je polomer kruhového oblúka. Veľkosť pravého uhla je v oblúkovej miere rovná <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\pi }{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>&#x3c0;<!-- π --></mi> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\pi }{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98f98bef5d4981ff6e2aa827d4699e347fb30db2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:2.168ex; height:4.676ex;" alt="{\displaystyle {\frac {\pi }{2}}}" /></span>. </p><p>Uhlová jednotka oblúkovej miery je v <a href="/wiki/Radi%C3%A1n" title="Radián">radiánoch</a> (skratka <i>rad</i>). </p> <div class="mw-heading mw-heading3"><h3 id="Stupňová_miera"><span id="Stup.C5.88ov.C3.A1_miera"></span>Stupňová miera</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Uhol&amp;veaction=edit&amp;section=8" title="Upraviť sekciu: Stupňová miera" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Uhol&amp;action=edit&amp;section=8" title="Editovat zdrojový kód sekce Stupňová miera"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Stupňová miera je určená tak, že pravý uhol je rozdelený na 90 dielov, ktoré sa nazývajú <i><a href="/wiki/Uhlov%C3%BD_stupe%C5%88" class="mw-redirect" title="Uhlový stupeň">(uhlové) stupne</a></i>. Vzťah medzi stupňovou a oblúkovou mierou je možné zapísať ako </p> <dl><dd>1° = π/180 rad</dd></dl> <p>Uhlový stupeň sa delí na 60 <i>(uhlových) <a href="/wiki/Min%C3%BAta" title="Minúta">minút</a></i>, tzn. 1°=60′, a každá uhlová minúta sa delí na 60 <i>(uhlových) <a href="/wiki/Sekunda" title="Sekunda">sekúnd</a></i>, tzn. 1′=60′′. </p> <div class="mw-heading mw-heading3"><h3 id="Stotinná_miera"><span id="Stotinn.C3.A1_miera"></span>Stotinná miera</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Uhol&amp;veaction=edit&amp;section=9" title="Upraviť sekciu: Stotinná miera" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Uhol&amp;action=edit&amp;section=9" title="Editovat zdrojový kód sekce Stotinná miera"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Stotinná miera je určená tak, že pravý uhol je rozdelený na 100 dielov, ktoré nazývame <a href="/wiki/Grad_(uhol)" title="Grad (uhol)">grady</a>, gony alebo stotinné stupne. Vzťah medzi stotinnou a oblúkovou mierou je možné zapísať ako </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1^{g}={\frac {\pi }{200}}rad}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>&#x3c0;<!-- π --></mi> <mn>200</mn> </mfrac> </mrow> <mi>r</mi> <mi>a</mi> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1^{g}={\frac {\pi }{200}}rad}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0db9db70bfe47ce77c06427eb641e35d387b5049" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:13.1ex; height:4.676ex;" alt="{\displaystyle 1^{g}={\frac {\pi }{200}}rad}" /></span></dd></dl> <p>Vzťah medzi 100-tinnou a 60-tinnou (stupňovou) mierou vyjadruje </p><p>1<sup>g</sup> = 9/10<sup>0</sup> = 0,9<sup>0</sup> </p><p>1<sup>0</sup> = 10/9 <sup>g</sup> </p><p>Ďalej pozri článok <a href="/wiki/Grad_(uhol)" title="Grad (uhol)">grad (uhol)</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Príklady"><span id="Pr.C3.ADklady"></span>Príklady</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Uhol&amp;veaction=edit&amp;section=10" title="Upraviť sekciu: Príklady" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Uhol&amp;action=edit&amp;section=10" title="Editovat zdrojový kód sekce Príklady"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Jeden stupeň je 1/180 priameho uhla, čiže priamy uhol má veľkosť 180°. Zlomky stupňov sa vyjadrujú buď v desiatkovej, alebo v šesťdesiatkovej <a href="/w/index.php?title=%C4%8C%C3%ADselnej_s%C3%BAstave&amp;action=edit&amp;redlink=1" class="new" title="Číselnej sústave (stránka neexistuje)">sústave</a>, pozri nasledujúce príklady: </p> <ul><li>pol stupňa = 0,5° = 0° 30’ t. j. 30 uhlových <a href="/wiki/Min%C3%BAta" title="Minúta">minút</a></li> <li>osmina stupňa = 0,125° = 0° 7’ 30" t. j. 7 uhlových minút a 30 <a href="/wiki/Sekunda" title="Sekunda">sekúnd</a>.</li></ul> <p>Jeden radián je 1/π priameho uhla. </p><p><span class="mw-default-size" typeof="mw:File"><a href="/wiki/S%C3%BAbor:VelikostUhlu.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/9/9a/VelikostUhlu.jpg" decoding="async" width="115" height="51" class="mw-file-element" data-file-width="115" data-file-height="51" /></a></span> </p><p>Veľkosť ďalších uhlov: </p> <ul><li>Nulový uhol: 0°, tzn. 0 rad</li> <li>Ostrý uhol: medzi 0° a 90°, tzn. medzi 0 a π/2 rad</li> <li>Pravý uhol: 90°, tzn. π/2</li> <li>Tupý uhol: medzi 90° a 180°, tzn. π/2 a π rad</li> <li>Kosý uhol: 0°&lt;α&lt;90° alebo 90°&lt;α&lt;180°</li> <li>Dutý uhol: 0°&lt;α&lt;180°</li> <li>Konvexný uhol: 0°≤α≤180°</li> <li>Nekonvexný (vypuklý) uhol: medzi 180° a 360°, tzn. π a 2π rad</li> <li>Priamy uhol: 180°, tzn. π rad</li> <li>Plný uhol: 360°, tzn. 2π rad</li></ul> <p>Stupne sa používajú predovšetkým z historických dôvodov a tiež pre relatívne ľahké vykonávanie jednoduchých výpočtov. Radiány majú výhodu pri zložitejších výpočtoch&#160;–&#160;zvlášť pri derivovaní či integrácii nie je potrebné počítať so špeciálnymi konštantami. Radián je navyše relatívne intuitívna jednotka. Vyjadruje priamo dĺžku oblúka, vytýčeného daným uhlom na <a href="/wiki/Jednotkov%C3%A1_kru%C5%BEnica" title="Jednotková kružnica">jednotkovej kružnici</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Veľkosť_orientovaného_uhla"><span id="Ve.C4.BEkos.C5.A5_orientovan.C3.A9ho_uhla"></span>Veľkosť orientovaného uhla</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Uhol&amp;veaction=edit&amp;section=11" title="Upraviť sekciu: Veľkosť orientovaného uhla" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Uhol&amp;action=edit&amp;section=11" title="Editovat zdrojový kód sekce Veľkosť orientovaného uhla"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Veľkosť orientovaného uhla je (v oblúkovej miere) rovná <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha +k2\pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x3b1;<!-- α --></mi> <mo>+</mo> <mi>k</mi> <mn>2</mn> <mi>&#x3c0;<!-- π --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha +k2\pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cac597643fd9300961b1612ddd8843b831f9dd53" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:8.034ex; height:2.343ex;" alt="{\displaystyle \alpha +k2\pi }" /></span>, kde <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x3b1;<!-- α --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }" /></span> je veľkosť rovnakého neorientovaného uhla a <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}" /></span> je <a href="/wiki/Cel%C3%A9_%C4%8D%C3%ADslo" title="Celé číslo">celé číslo</a>. Veľkosť orientovaného uhla je uhol, ktorým musí prejsť počiatočné rameno pri otočení do koncového ramena. Člen <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k2\pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> <mn>2</mn> <mi>&#x3c0;<!-- π --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k2\pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/714c5acd3d41e82dae540a68e19af91323555beb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.706ex; height:2.176ex;" alt="{\displaystyle k2\pi }" /></span> predstavuje počet celých otáčok okolo vrcholu uhla. </p> <div class="mw-heading mw-heading2"><h2 id="Operácie_s_uhlami"><span id="Oper.C3.A1cie_s_uhlami"></span>Operácie s uhlami</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Uhol&amp;veaction=edit&amp;section=12" title="Upraviť sekciu: Operácie s uhlami" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Uhol&amp;action=edit&amp;section=12" title="Editovat zdrojový kód sekce Operácie s uhlami"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Sčítanie uhlov</b> </p> <ul><li>Dva uhly sa sčítajú tak, že vezmete kružidlo a ľubovoľne ním pretnite uhol ktorý máte narysovaný, kružidlo zapichnite ne ľubovoľné miesto na dolnej čiare a prejdite čiarou k čiare 2.</li> <li>Dole na uhla od čiary kružidla zapichnite kružidlo do dolnej čiary do miesta kde sa pretínajú čiary uhla a kružidla a druhý koniec kružidla na druhú čiaru kde sa pretína čiara uhla a kružidla a nechajte v kružidle veľkosť ktorú ste si z uhla vytiahli.</li> <li>Ak máte 2 uhly na sčítanie nechajte si ešte stále veľkosť kružidla z prvého uhla a na druhom narysujte tak že ľubovoľne zapichnete kružidlo s veľkosťou z minulého uhla na čiaru druhého uhla a nakreslite oblúk na druhú čiaru a veľkosť na kružidle si o opäť ponechajte.</li> <li>Narysujte čiaru s jedným bodom a kružidlo so stále rovnakou veľkosťou zapichnite do bodu (bod musí byť na ľavej strane) a narysujte kružidlom oblúk doľava.</li> <li>Na oboch uhloch zanikli ramená tam kde sa pretína oblúk kružidla a uhol tak tam zapichnite kružidlo a nakreslite oblúk do druhého ramena. Nechajte si veľkosť a zapichnite kružidlo na narysovanú čiaru a na bode zapichnite a narysujte oblúk do predchádzajúceho oblúka od kružidla než sa stretnú a potom odtiaľ kde sa stretli pravítkom narysujte čiaru do bodu a to isté s druhým uhlom a na obrázku vidíte výsledok.</li></ul> <p><b>Odčítanie uhlov</b> </p> <ul><li>Dva uhly sa odčítajú tak, že sa jedným ramenom priložia dovnútra seba a výsledný uhol vznikne medzi druhými dvoma ramenami. Výpočtovo stačí odčítať veľkosti uhlov.</li></ul> <p><span typeof="mw:File"><a href="/wiki/S%C3%BAbor:OdcitaniUhluSK.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/OdcitaniUhluSK.jpg/500px-OdcitaniUhluSK.jpg" decoding="async" width="350" height="145" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/OdcitaniUhluSK.jpg/525px-OdcitaniUhluSK.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/e/e3/OdcitaniUhluSK.jpg 2x" data-file-width="563" data-file-height="234" /></a></span> </p><p><b>Násobenie uhlov prirodzeným číslom</b> </p> <ul><li>Násobenie uhla <a href="/wiki/Prirodzen%C3%A9_%C4%8D%C3%ADslo" title="Prirodzené číslo">prirodzeným číslom</a> sa vykonáva na opakované sčítanie toho istého uhla toľkokrát, koľko je dané prirodzené číslo. Číselne sa vynásobí veľkosť uhla daným prirodzeným číslom.</li></ul> <p><b>Delenie uhlov dvoma</b> </p> <ul><li>Uhol sa delí dvoma zostrojením <a href="/wiki/Os_(geometria)" title="Os (geometria)">osi uhla</a>. číselne sa vydelí veľkosť uhla dvoma. Konštrukčne nie je možné vykonať presné delenie všeobecného uhla troma, úloha je známa pod menom <a href="/wiki/Trisekcia_uhla" title="Trisekcia uhla">trisekcia uhla</a>.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Operácie_s_orientovanými_uhlami"><span id="Oper.C3.A1cie_s_orientovan.C3.BDmi_uhlami"></span>Operácie s orientovanými uhlami</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Uhol&amp;veaction=edit&amp;section=13" title="Upraviť sekciu: Operácie s orientovanými uhlami" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Uhol&amp;action=edit&amp;section=13" title="Editovat zdrojový kód sekce Operácie s orientovanými uhlami"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pri operáciách s orientovanými uhlami je nutné zohľadniť ich znamienka. </p><p>Ak teda k orientovanému uhlu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x3b1;<!-- α --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }" /></span> pripočítame orientovaný uhol <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x3b2;<!-- β --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }" /></span>, ktorý je však opačne orientovaný, je výsledok rovnaký ako by sme od neorientovaného uhla o rovnakej veľkosti ako má uhol <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x3b1;<!-- α --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }" /></span> odčítali neorientovaný uhol o rovnakej veľkosti ako má uhol <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x3b2;<!-- β --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }" /></span>. Výsledkom takejto operácie je opäť orientovaný uhol, ktorý má rovnakú orientáciu ako <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x3b1;<!-- α --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }" /></span>, ak <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha &gt;\beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x3b1;<!-- α --></mi> <mo>&gt;</mo> <mi>&#x3b2;<!-- β --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha &gt;\beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/878aa4ba937a08258b46361229c9c35d970672ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.918ex; height:2.509ex;" alt="{\displaystyle \alpha &gt;\beta }" /></span>, má orientáciu ako uhol <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x3b2;<!-- β --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }" /></span>, ak <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha &lt;\beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x3b1;<!-- α --></mi> <mo>&lt;</mo> <mi>&#x3b2;<!-- β --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha &lt;\beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bc4250c976810fd3abc5916c47ee4984a7e5882b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.918ex; height:2.509ex;" alt="{\displaystyle \alpha &lt;\beta }" /></span>. </p> <div class="mw-heading mw-heading2"><h2 id="Meracie_prístroje"><span id="Meracie_pr.C3.ADstroje"></span>Meracie prístroje</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Uhol&amp;veaction=edit&amp;section=14" title="Upraviť sekciu: Meracie prístroje" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Uhol&amp;action=edit&amp;section=14" title="Editovat zdrojový kód sekce Meracie prístroje"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Meranie a určovanie uhlov je v praxi veľmi dôležité. Využíva ich <a href="/wiki/Astron%C3%B3mia" title="Astronómia">astronómia</a>, <a href="/wiki/Geod%C3%A9zia" title="Geodézia">geodézia</a> a mnoho ďalších odborov. Preto sa tiež vyvinul rad meracích prístrojov. </p> <ul><li>uhlomer&#160;–&#160;najjednoduchšie meradlo&#160;–&#160;ide o polkruhovú dosku so stupnicou po obvode. Zložitějšie prístroje majú pohyblivé rameno.</li> <li>Jakubova palica&#160;–&#160;jednoduchý stredoveký astronomický prístroj merajúca na princípe porovnávania strán trojuholníka</li> <li><a href="/wiki/Kvadrant_(astron%C3%B3mia)" title="Kvadrant (astronómia)">kvadrant</a>, <a href="/wiki/Sextant_(merac%C3%AD_pr%C3%ADstroj)" title="Sextant (merací prístroj)">sextant</a>, <a href="/wiki/Oktant_(astron%C3%B3mia)" title="Oktant (astronómia)">oktant</a>&#160;–&#160;používané v navigácii</li> <li>teodolit&#160;–&#160;základný prístroj používaný v geodézii na meranie a určovanie zvislých a vodorovných uhlov</li></ul> <div class="mw-heading mw-heading2"><h2 id="Pozri_aj">Pozri aj</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Uhol&amp;veaction=edit&amp;section=15" title="Upraviť sekciu: Pozri aj" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Uhol&amp;action=edit&amp;section=15" title="Editovat zdrojový kód sekce Pozri aj"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Priestorov%C3%BD_uhol" title="Priestorový uhol">Priestorový uhol</a></li> <li><a href="/wiki/Steradi%C3%A1n" title="Steradián">Steradián</a></li> <li><a href="/wiki/Trisekcia_uhla" title="Trisekcia uhla">Trisekcia uhla</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Iné_projekty"><span id="In.C3.A9_projekty"></span>Iné projekty</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Uhol&amp;veaction=edit&amp;section=16" title="Upraviť sekciu: Iné projekty" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Uhol&amp;action=edit&amp;section=16" title="Editovat zdrojový kód sekce Iné projekty"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="interProject commons" style="display:none;"><a href="https://commons.wikimedia.org/wiki/Category:Angles" class="extiw" title="commons:Category:Angles">Commons</a></div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Spolupracuj na&#160;Commons"><img alt="Spolupracuj na&#160;Commons" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png" decoding="async" width="18" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/27px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/36px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> Commons ponúka multimediálne súbory na&#160;tému <b><a href="https://commons.wikimedia.org/wiki/Category:Angles" class="extiw" title="commons:Category:Angles">uhly</a></b>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Externé_odkazy"><span id="Extern.C3.A9_odkazy"></span>Externé odkazy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Uhol&amp;veaction=edit&amp;section=17" title="Upraviť sekciu: Externé odkazy" class="mw-editsection-visualeditor"><span>upraviť</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Uhol&amp;action=edit&amp;section=17" title="Editovat zdrojový kód sekce Externé odkazy"><span>upraviť zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://cloud5.edupage.org/cloud/kniznica.pdf?z%3ArJAlYm4f4xVATjhTdpRa9N1l9u7YMW2o133pyVXOIKwhRRkFrTIv5MRF1BPud2U5">Stupňová a oblúková miera</a></li></ul> <!-- NewPP limit report Parsed by mw‐web.eqiad.main‐7fd96bd568‐w5s8m Cached time: 20250315090004 Cache expiry: 2592000 Reduced expiry: false Complications: [show‐toc] CPU time usage: 0.094 seconds Real time usage: 0.181 seconds Preprocessor visited node count: 1477/1000000 Post‐expand include size: 1381/2097152 bytes Template argument size: 353/2097152 bytes Highest expansion depth: 9/100 Expensive parser function count: 0/500 Unstrip recursion depth: 0/20 Unstrip post‐expand size: 1260/5000000 bytes Lua time usage: 0.019/10.000 seconds Lua memory usage: 1376321/52428800 bytes Number of Wikibase entities loaded: 1/400 --> <!-- Transclusion expansion time report (%,ms,calls,template) 100.00% 64.169 1 -total 90.66% 58.175 1 Šablóna:Projekt 11.43% 7.334 1 Šablóna:Projekt/odkaz 8.64% 5.543 21 Šablóna:Projekt/box 6.24% 4.002 20 Šablóna:Projekt/param 5.10% 3.274 1 Šablóna:Clear 2.73% 1.752 1 Šablóna:Pozri --> <!-- Saved in parser cache with key skwiki:pcache:102797:|#|:idhash:canonical and timestamp 20250315090004 and revision id 7937282. 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