{"id":6752,"date":"2024-06-22T12:37:03","date_gmt":"2024-06-22T15:37:03","guid":{"rendered":"https:\/\/xequematenem.com.br\/blog\/?p=6752"},"modified":"2024-06-22T12:37:03","modified_gmt":"2024-06-22T15:37:03","slug":"questao-142-enem-ppl-2018","status":"publish","type":"post","link":"https:\/\/xequematenem.com.br\/blog\/questao-142-enem-ppl-2018\/","title":{"rendered":"Quest\u00e3o 142 &#8211; ENEM PPL 2018"},"content":{"rendered":"\n<p class=\"has-text-align-center wp-block-paragraph\">Quest\u00e3o 142 &#8211; Geometria Plana<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">As Artes Marciais Mistas, tradu\u00e7\u00e3o do ingl\u00eas: MMA \u2013 mixed martial arts, s\u00e3o realizadas num oct\u00f3gono regular. De acordo com a figura, em certo momento os dois lutadores est\u00e3o respectivamente nas <strong>posi\u00e7\u00f5es G e F, e o juiz est\u00e1 na posi\u00e7\u00e3o I.<\/strong> <strong>O tri\u00e2ngulo IGH \u00e9 equil\u00e1tero e G\u00ceF \u00e9 o \u00e2ngulo formado pelas semirretas com origem na posi\u00e7\u00e3o do juiz, respectivamente passando pelas posi\u00e7\u00f5es de cada um dos lutadores.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"223\" height=\"212\" data-src=\"https:\/\/xequematenem.com.br\/blog\/wp-content\/uploads\/2024\/06\/image-84.png\" alt=\"\" class=\"wp-image-6753 lazyload\" title=\"\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 223px; --smush-placeholder-aspect-ratio: 223\/212;\"><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">A medida do \u00e2ngulo G\u00ceF \u00e9&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A) 120\u00b0&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B) 75\u00b0&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C) 67,5\u00b0&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D) 60\u00b0&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">E) 52,5\u00b0<\/p>\n\n\n\n<p class=\"has-text-align-center has-large-font-size wp-block-paragraph\"><strong>Resolu\u00e7\u00e3o<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Se IGH \u00e9 equil\u00e1tero, ent\u00e3o<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">GH = GI&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Se temos um oct\u00f3gono regular, posso afirmar que&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">GH = FG<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Consequentemente<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">FG = GI<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ou seja, o tri\u00e2ngulo GIF \u00e9 is\u00f3sceles com base em FI, portanto os \u00e2ngulos GIF e GFI s\u00e3o iguais.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Basta descobrir o valor do \u00e2ngulo IGF para descobrir o valor dos outros dois \u00e2ngulos.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Podemos calcular o valor do \u00e2ngulo FGH usando a f\u00f3rmula de \u00e2ngulos internos de um pol\u00edgono<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(n -2)180\/n<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Como \u00e9 um oct\u00f3gono, n=8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">FGH = (8-2)180\/8 = 135<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Se o tri\u00e2ngulo GIH \u00e9 equil\u00e1tero, todos os \u00e2ngulos s\u00e3o 60, ent\u00e3o<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">IGH = 60<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sendo<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">IGF = FGH &#8211; IGH<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Temos que<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">IGF = 135 &#8211; 60<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">IGF = 75<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sabemos que a soma dos \u00e2ngulos internos de um tri\u00e2ngulo \u00e9 180, ent\u00e3o<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">IGF + GIF + GFI = 180<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Se&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">GIF = GFI&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">como falamos anteriormente, ent\u00e3o<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">IGF + 2.GIF = 180<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Substituindo o valor de IGF<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">75 + 2.GIF = 180<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2.GIF = 105<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">GIF = 52,5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Alternativa E<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Quest\u00e3o 142 &#8211; Geometria Plana As Artes Marciais Mistas, tradu\u00e7\u00e3o do ingl\u00eas: MMA \u2013 mixed martial arts, s\u00e3o realizadas num oct\u00f3gono regular. De acordo com a figura, em certo momento os dois lutadores est\u00e3o respectivamente nas posi\u00e7\u00f5es G e F, e o juiz est\u00e1 na posi\u00e7\u00e3o I. O tri\u00e2ngulo IGH \u00e9 equil\u00e1tero e G\u00ceF \u00e9 [&hellip;]<\/p>\n","protected":false},"author":11,"featured_media":6753,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[87,97],"tags":[],"area-do-conhecimento":[132,118],"assunto":[50],"class_list":["post-6752","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-questoes-ppl","category-2018-questoes-ppl","area-do-conhecimento-matematica","area-do-conhecimento-matematica-e-suas-tecnologias","assunto-geometria-plana"],"_links":{"self":[{"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/posts\/6752","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/users\/11"}],"replies":[{"embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/comments?post=6752"}],"version-history":[{"count":1,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/posts\/6752\/revisions"}],"predecessor-version":[{"id":6754,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/posts\/6752\/revisions\/6754"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/media\/6753"}],"wp:attachment":[{"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/media?parent=6752"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/categories?post=6752"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/tags?post=6752"},{"taxonomy":"area-do-conhecimento","embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/area-do-conhecimento?post=6752"},{"taxonomy":"assunto","embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/assunto?post=6752"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}