\nEnunciado<\/b><\/span><\/p>\n
Determina quantos lados tem um pol\u00edgono regular cujo \u00e2ngulo interno mede:<\/p>\n
\n
140 graus<\/li>\n
135 graus<\/li>\n<\/ol>\n
Resolu\u00e7\u00e3o >><\/a><\/span><\/div><\/div>\n\n
\nResolu\u00e7\u00e3o<\/b><\/span><\/p>\n
\n
A soma das amplitudes, em graus, dos \u00e2ngulos internos de um pol\u00edgono convexo com \$n\$ lados \u00e9 igual a\u00a0\${S_i} = \\left( {n – 2} \\right) \\times 180^\\circ \$. de um pol\u00edgono convexo com \$n\$ lados \u00e9 igual a\u00a0\${S_i} = \\left( {n – 2} \\right) \\times 180^\\circ \$.<\/p>\n<\/blockquote>\n
\n
Como o pol\u00edgono \u00e9 regular, a amplitude de qualquer um dos seus $n$ \u00e2ngulos internos resultar\u00e1 da divis\u00e3o da\u00a0soma das amplitudes dos \u00e2ngulos internos por $n$. Neste caso, o pol\u00edgono considerado tem 9 lados:
\n\\[\\begin{array}{*{20}{l}}{\\alpha = 140^\\circ }& \\Leftrightarrow &{\\frac{{\\left( {n – 2} \\right) \\times 180^\\circ }}{n} = 140^\\circ }\\\\{}& \\Leftrightarrow &{n \\times 180^\\circ – 360^\\circ = n \\times 140^\\circ }\\\\{}& \\Leftrightarrow &{n = \\frac{{360^\\circ }}{{40^\\circ }}}\\\\{}& \\Leftrightarrow &{n = 9}\\end{array}\\]<\/li>\n
Como o pol\u00edgono \u00e9 regular, a amplitude de qualquer um dos seus $n$ \u00e2ngulos internos resultar\u00e1 da divis\u00e3o da\u00a0soma das amplitudes dos \u00e2ngulos internos por $n$. Neste caso, o pol\u00edgono considerado tem 8 lados:
\n\\[\\begin{array}{*{20}{l}}{\\alpha = 135^\\circ }& \\Leftrightarrow &{\\frac{{\\left( {n – 2} \\right) \\times 180^\\circ }}{n} = 135^\\circ }\\\\{}& \\Leftrightarrow &{n \\times 180^\\circ – 360^\\circ = n \\times 135^\\circ }\\\\{}& \\Leftrightarrow &{n = \\frac{{360^\\circ }}{{45^\\circ }}}\\\\{}& \\Leftrightarrow &{n = 8}\\end{array}\\]<\/li>\n<\/ol>\n
<< Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"
Enunciado Resolu\u00e7\u00e3o Enunciado Determina quantos lados tem um pol\u00edgono regular cujo \u00e2ngulo interno mede: 140 graus 135 graus Resolu\u00e7\u00e3o >> Resolu\u00e7\u00e3o << Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20485,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,278],"tags":[426,464,188],"series":[],"class_list":["post-13392","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-circunferencia-e-poligonos","tag-9-o-ano","tag-angulo-interno","tag-circunferencia"],"views":3385,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag143-6_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13392","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=13392"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13392\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20485"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13392"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13392"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13392"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13392"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}