{"id":2641,"date":"2026-10-15T00:41:31","date_gmt":"2026-10-14T23:41:31","guid":{"rendered":"https:\/\/wpcalc.com\/pl\/matematyka\/katy-wewnetrzne-wielokata\/"},"modified":"2026-10-15T00:41:31","modified_gmt":"2026-10-14T23:41:31","slug":"katy-wewnetrzne-wielokata","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/pl\/matematyka\/katy-wewnetrzne-wielokata\/","title":{"rendered":"Kalkulator k\u0105t\u00f3w wewn\u0119trznych wielok\u0105ta"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Oblicz sum\u0119 k\u0105t\u00f3w wewn\u0119trznych wielok\u0105ta<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"2641\" data-favorite-title=\"K\u0105ty wewn\u0119trzne wielok\u0105ta\" data-favorite-url=\"https:\/\/wpcalc.com\/pl\/matematyka\/katy-wewnetrzne-wielokata\/\" data-favorite-excerpt=\"Wpisz liczb\u0119 bok\u00f3w, aby obliczy\u0107 sum\u0119 k\u0105t\u00f3w wewn\u0119trznych dowolnego wielok\u0105ta. Dla wielok\u0105ta foremnego otrzymasz te\u017c ka\u017cdy k\u0105t wewn\u0119trzny i zewn\u0119trzny wraz z krokami oblicze\u0144.\" aria-label=\"Dodaj do ulubionych\" data-favorite-icon=\"icon icon-geometry\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/pl\/matematyka\/katy-wewnetrzne-wielokata\/\" method=\"POST\" class=\"calculator\" id=\"calculator-2641\" data-post=\"2641\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Pola danych<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Liczba bok\u00f3w (n)<\/label><div class=\"term\">n<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"liczba_bokw_n\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"6\" min=\"3\" value=\"6\"\/><small id=\"calc-info-1\">Wielok\u0105t ma co najmniej 3 boki (tr\u00f3jk\u0105t).<\/small><\/div><div class=\"field is-checkbox\" id=\"input-2\"><input type=\"checkbox\" id=\"field-2\" value=\"1\" checked=\"checked\"\/><label for=\"field-2\">Wielok\u0105t foremny<\/label><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Przelicz ponownie\" id=\"calculate-button\" data-post=\"2641\">Oblicz<\/button><button type=\"reset\">Wyczy\u015b\u0107<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Obliczaj automatycznie<\/label><small>Po w\u0142\u0105czeniu wynik aktualizuje si\u0119 automatycznie po zmianie dowolnej warto\u015bci.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> K\u0105ty Twojego wielok\u0105ta<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Suma k\u0105t\u00f3w wewn\u0119trznych<\/span><span class=\"result-term\">\u03a3\u03b1<\/span><\/span><span class=\"field-value\" id=\"result-1\" data-unit=\"\u00b0\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>Ka\u017cdy k\u0105t wewn\u0119trzny<\/span><span class=\"result-term\">\u03b1<\/span><\/span><span class=\"field-value\" id=\"result-2\" data-unit=\"\u00b0\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-3\"><span class=\"field-title\"><span>Ka\u017cdy k\u0105t zewn\u0119trzny<\/span><span class=\"result-term\">\u03b2<\/span><\/span><span class=\"field-value\" id=\"result-3\" data-unit=\"\u00b0\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-4\"><span class=\"field-title\"><span>Kroki oblicze\u0144<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Kopiuj link do tego obliczenia<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Zostaw komentarz<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"2641\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Jak oceniasz ten wynik?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Lubi\u0119 to <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Pomocne <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Niejasne <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Rozczarowanie <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Niedok\u0142adne <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Wz\u00f3r na k\u0105ty wewn\u0119trzne wielok\u0105ta<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Wz\u00f3r<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ \\Sigma\\alpha = (n - 2) \\cdot 180^\\circ \\qquad \\alpha = \\frac{(n - 2) \\cdot 180^\\circ}{n} \\qquad \\beta = \\frac{360^\\circ}{n} \\]<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>gdzie:<\/strong><\/p>\n<ul>\n<li>\\(n\\) \u2014 liczba bok\u00f3w wielok\u0105ta (\\(n \\ge 3\\))<\/li>\n<li>\\(\\Sigma\\alpha\\) \u2014 suma wszystkich k\u0105t\u00f3w wewn\u0119trznych (w stopniach)<\/li>\n<li>\\(\\alpha\\) \u2014 ka\u017cdy k\u0105t wewn\u0119trzny wielok\u0105ta <em>foremnego<\/em> (w stopniach)<\/li>\n<li>\\(\\beta\\) \u2014 ka\u017cdy k\u0105t zewn\u0119trzny wielok\u0105ta <em>foremnego<\/em> (w stopniach)<\/li>\n<\/ul>\n<p>Pierwszy wz\u00f3r podaje sum\u0119 wszystkich k\u0105t\u00f3w wewn\u0119trznych dowolnego wielok\u0105ta \u2014 foremnego lub nieforemnego \u2014 wy\u0142\u0105cznie na podstawie liczby bok\u00f3w. Pozosta\u0142e dwa wzory dotycz\u0105 wielok\u0105t\u00f3w foremnych, w kt\u00f3rych wszystkie k\u0105ty s\u0105 r\u00f3wne, wi\u0119c wystarczy podzieli\u0107 sum\u0119 r\u00f3wno mi\u0119dzy \\(n\\) k\u0105t\u00f3w.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>K\u0105ty wewn\u0119trzne wielok\u0105ta \u2014 przyk\u0142ad obliczenia<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Przyk\u0142ad:<\/strong> sze\u015bciok\u0105t foremny (warto\u015b\u0107 domy\u015blna kalkulatora), kt\u00f3ry ma \\(n = 6\\) r\u00f3wnych bok\u00f3w i r\u00f3wnych k\u0105t\u00f3w.<\/p>\n<p>\\[ \\Sigma\\alpha = (6 - 2) \\cdot 180^\\circ = 4 \\cdot 180^\\circ = 720^\\circ \\]<\/p>\n<p>\\[ \\alpha = \\frac{720^\\circ}{6} = 120^\\circ \\]<\/p>\n<p>\\[ \\beta = \\frac{360^\\circ}{6} = 60^\\circ \\]<\/p>\n<p><strong>Wynik:<\/strong> k\u0105ty wewn\u0119trzne sze\u015bciok\u0105ta sumuj\u0105 si\u0119 do <strong>720\u00b0<\/strong>; ka\u017cdy k\u0105t wewn\u0119trzny sze\u015bciok\u0105ta foremnego ma <strong>120\u00b0<\/strong>, a ka\u017cdy k\u0105t zewn\u0119trzny <strong>60\u00b0<\/strong>. Zauwa\u017c, \u017ce \\(120^\\circ + 60^\\circ = 180^\\circ\\) \u2014 tak jak zawsze dla pary k\u0105t\u00f3w wewn\u0119trznego i zewn\u0119trznego.<\/p>\n<p>\n\r\n<\/section>\n<h2>Jak korzysta\u0107 z kalkulatora<\/h2>\n<ol>\n<li>Wpisz <strong>liczb\u0119 bok\u00f3w (n)<\/strong> \u2014 dowoln\u0105 liczb\u0119 ca\u0142kowit\u0105 od 3 w g\u00f3r\u0119, na przyk\u0142ad 6 dla sze\u015bciok\u0105ta.<\/li>\n<li>Zostaw zaznaczone pole <strong>\u201ewielok\u0105t foremny\u201d<\/strong>, je\u015bli wszystkie boki i wszystkie k\u0105ty s\u0105 r\u00f3wne; odznacz je dla wielok\u0105ta nieforemnego.<\/li>\n<li>Odczytaj <strong>sum\u0119 k\u0105t\u00f3w wewn\u0119trznych<\/strong> w stopniach \u2014 jest poprawna dla ka\u017cdego wielok\u0105ta o tej liczbie bok\u00f3w.<\/li>\n<li>Gdy opcja \u201ewielok\u0105t foremny\u201d jest zaznaczona, odczytaj dodatkowo <strong>ka\u017cdy k\u0105t wewn\u0119trzny<\/strong> i <strong>ka\u017cdy k\u0105t zewn\u0119trzny<\/strong>.<\/li>\n<li>Zajrzyj do <strong>krok\u00f3w oblicze\u0144<\/strong>, aby zobaczy\u0107 pe\u0142ne rachunki wraz z nazw\u0105 wielok\u0105ta, je\u015bli ma on 12 bok\u00f3w lub mniej.<\/li>\n<\/ol>\n<h2>Czym s\u0105 k\u0105ty wewn\u0119trzne wielok\u0105ta?<\/h2>\n<p>K\u0105t wewn\u0119trzny to k\u0105t wewn\u0105trz wielok\u0105ta przy danym wierzcho\u0142ku, mi\u0119dzy dwoma bokami, kt\u00f3re si\u0119 w nim spotykaj\u0105. Ka\u017cdy wielok\u0105t o \\(n\\) bokach ma dok\u0142adnie \\(n\\) k\u0105t\u00f3w wewn\u0119trznych \u2014 tr\u00f3jk\u0105t ma 3, sze\u015bciok\u0105t ma 6 i tak dalej.<\/p>\n<p>Najwa\u017cniejszy jest fakt, \u017ce <em>suma<\/em> tych k\u0105t\u00f3w zale\u017cy wy\u0142\u0105cznie od liczby bok\u00f3w, a nie od kszta\u0142tu wielok\u0105ta. K\u0105ty tr\u00f3jk\u0105ta zawsze sumuj\u0105 si\u0119 do 180\u00b0, niezale\u017cnie od tego, czy jest on chudy i wyd\u0142u\u017cony, czy idealnie r\u00f3wnoboczny. Ka\u017cdy kolejny bok dodaje 180\u00b0 do sumy: 180\u00b0 dla tr\u00f3jk\u0105ta, 360\u00b0 dla czworok\u0105ta, 540\u00b0 dla pi\u0119ciok\u0105ta, 720\u00b0 dla sze\u015bciok\u0105ta. W\u0142a\u015bnie to koduje wz\u00f3r \\((n - 2) \\cdot 180^\\circ\\) \u2014 wielok\u0105t mo\u017cna podzieli\u0107 na \\(n - 2\\) tr\u00f3jk\u0105ty, z kt\u00f3rych ka\u017cdy wnosi 180\u00b0.<\/p>\n<p>W wielok\u0105cie <strong>nieforemnym<\/strong> sta\u0142a jest tylko suma; poszczeg\u00f3lne k\u0105ty mog\u0105 by\u0107 dowolne, byle razem dawa\u0142y t\u0119 sum\u0119. W wielok\u0105cie <strong>foremnym<\/strong> \u2014 o r\u00f3wnych bokach i r\u00f3wnych k\u0105tach \u2014 ka\u017cdy k\u0105t to po prostu suma podzielona przez \\(n\\), a ka\u017cdy k\u0105t zewn\u0119trzny to \\(360^\\circ \/ n\\), poniewa\u017c k\u0105ty zewn\u0119trzne musz\u0105 razem da\u0107 pe\u0142ny obr\u00f3t wok\u00f3\u0142 wielok\u0105ta.<\/p>\n<p>Wyniki przydaj\u0105 si\u0119 przy zadaniach z geometrii, w pracach glazbiarskich i projektowych oraz na budowie. Na przyk\u0142ad \u015bwiadomo\u015b\u0107, \u017ce ka\u017cdy k\u0105t wewn\u0119trzny sze\u015bciok\u0105ta foremnego ma 120\u00b0, wyja\u015bnia, dlaczego trzy sze\u015bciok\u0105ty idealnie stykaj\u0105 si\u0119 wok\u00f3\u0142 jednego punktu (3 \u00d7 120\u00b0 = 360\u00b0) \u2014 to w\u0142a\u015bnie podstawa plastra miodu.<\/p>\n<h2>Za\u0142o\u017cenia, ograniczenia i wskaz\u00f3wki<\/h2>\n<ul>\n<li><strong>Wielok\u0105ty wypuk\u0142e:<\/strong> wzory zak\u0142adaj\u0105 wielok\u0105t prosty. Dla wielok\u0105t\u00f3w wkl\u0119s\u0142ych (niewypuk\u0142ych) wz\u00f3r na sum\u0119 nadal obowi\u0105zuje, ale jeden lub wi\u0119cej k\u0105t\u00f3w wewn\u0119trznych przekracza 180\u00b0.<\/li>\n<li><strong>Wielok\u0105ty samoprzecinaj\u0105ce si\u0119:<\/strong> (jak pi\u0119cioramienna gwiazda wykre\u015blona jedn\u0105 ci\u0105g\u0142\u0105 lini\u0105) te wzory ich nie dotycz\u0105.<\/li>\n<li><strong>Tylko liczby ca\u0142kowite:<\/strong> wielok\u0105t nie mo\u017ce mie\u0107 u\u0142amkowej liczby bok\u00f3w, dlatego kalkulator wymaga liczby ca\u0142kowitej r\u00f3wnej co najmniej 3.<\/li>\n<li><strong>K\u0105ty zewn\u0119trzne:<\/strong> podany k\u0105t zewn\u0119trzny dotyczy wielok\u0105ta foremnego. W ka\u017cdym wielok\u0105cie wypuk\u0142ym k\u0105ty zewn\u0119trzne nadal sumuj\u0105 si\u0119 do 360\u00b0, ale pojedynczo r\u00f3\u017cni\u0105 si\u0119, je\u015bli wielok\u0105t jest nieforemny.<\/li>\n<li><strong>Du\u017ce warto\u015bci:<\/strong> wraz ze wzrostem \\(n\\) ka\u017cdy k\u0105t wewn\u0119trzny wielok\u0105ta foremnego zbli\u017ca si\u0119 do 180\u00b0, a ka\u017cdy k\u0105t zewn\u0119trzny do 0\u00b0 \u2014 wielok\u0105t foremny o wielu bokach wygl\u0105da ju\u017c prawie jak okr\u0105g.<\/li>\n<\/ul>\n<p>Przydatny fakt pokrewny: liczba przek\u0105tnych \\(n\\)-k\u0105ta to \\(\\frac{n(n-3)}{2}\\), co wynika z wyboru 2 wierzcho\u0142k\u00f3w spo\u015br\u00f3d \\(n\\) \u2014 tego typu zliczanie mo\u017cesz \u0107wiczy\u0107 w naszym <a href=\"https:\/\/wpcalc.com\/pl\/matematyka\/wspolczynnik-dwumianowy\/\">kalkulatorze wsp\u00f3\u0142czynnika dwumianowego<\/a>. Je\u015bli lubisz narz\u0119dzia z liczbami i wzorami, wypr\u00f3buj te\u017c <a href=\"https:\/\/wpcalc.com\/pl\/matematyka\/generator-kwadratu-magicznego\/\">generator kwadrat\u00f3w magicznych<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Wpisz liczb\u0119 bok\u00f3w, aby obliczy\u0107 sum\u0119 k\u0105t\u00f3w wewn\u0119trznych dowolnego wielok\u0105ta. Dla wielok\u0105ta foremnego otrzymasz te\u017c ka\u017cdy k\u0105t wewn\u0119trzny i zewn\u0119trzny wraz z krokami oblicze\u0144.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[6],"tags":[41],"class_list":["post-2641","post","type-post","status-publish","format-standard","hentry","category-matematyka","tag-geometria"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/2641","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/comments?post=2641"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/2641\/revisions"}],"predecessor-version":[{"id":2732,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/2641\/revisions\/2732"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/media?parent=2641"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/categories?post=2641"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/tags?post=2641"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}