{"id":232387,"date":"2025-06-12T00:14:35","date_gmt":"2025-06-12T00:14:35","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=232387"},"modified":"2025-06-12T00:14:37","modified_gmt":"2025-06-12T00:14:37","slug":"a-pentagon-has-two-right-angles-a-100-angle-and-a-120-angle","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/12\/a-pentagon-has-two-right-angles-a-100-angle-and-a-120-angle\/","title":{"rendered":"A pentagon has two right angles, a 100\u00b0 angle and a 120\u00b0 angle."},"content":{"rendered":"\n<p>A pentagon has two right angles, a 100\u00b0 angle and a 120\u00b0 angle. What is the measure of its fifth angle<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>A <strong>pentagon<\/strong> has 5 sides. The formula to find the sum of the interior angles of an <em>n<\/em>-sided polygon is:Sum&nbsp;of&nbsp;interior&nbsp;angles=(n\u22122)\u00d7180\u2218\\text{Sum of interior angles} = (n &#8211; 2) \\times 180^\\circSum&nbsp;of&nbsp;interior&nbsp;angles=(n\u22122)\u00d7180\u2218<\/p>\n\n\n\n<p>Substituting n=5n = 5n=5:(5\u22122)\u00d7180\u2218=3\u00d7180\u2218=540\u2218(5 &#8211; 2) \\times 180^\\circ = 3 \\times 180^\\circ = 540^\\circ(5\u22122)\u00d7180\u2218=3\u00d7180\u2218=540\u2218<\/p>\n\n\n\n<p>So, the total sum of the interior angles in a pentagon is <strong>540 degrees<\/strong>.<\/p>\n\n\n\n<p>Now, we are told that four of the five angles are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Two right angles: 90\u2218+90\u2218=180\u221890^\\circ + 90^\\circ = 180^\\circ90\u2218+90\u2218=180\u2218<\/li>\n\n\n\n<li>One angle of 100\u2218100^\\circ100\u2218<\/li>\n\n\n\n<li>One angle of 120\u2218120^\\circ120\u2218<\/li>\n<\/ul>\n\n\n\n<p>Let us now add these known angles:90\u2218+90\u2218+100\u2218+120\u2218=400\u221890^\\circ + 90^\\circ + 100^\\circ + 120^\\circ = 400^\\circ90\u2218+90\u2218+100\u2218+120\u2218=400\u2218<\/p>\n\n\n\n<p>Since the total must be 540\u00b0, we subtract the sum of the known angles from 540\u00b0 to find the measure of the fifth angle:540\u2218\u2212400\u2218=140\u2218540^\\circ &#8211; 400^\\circ = 140^\\circ540\u2218\u2212400\u2218=140\u2218<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p><strong>The measure of the fifth angle is 140 degrees.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>In geometry, the measure of the interior angles of a polygon can be determined using a standard formula. For any polygon with <em>n<\/em> sides, the sum of the interior angles is given by:(n\u22122)\u00d7180\u2218(n &#8211; 2) \\times 180^\\circ(n\u22122)\u00d7180\u2218<\/p>\n\n\n\n<p>This formula comes from the fact that any polygon can be divided into (n\u22122)(n &#8211; 2)(n\u22122) triangles, and each triangle has an angle sum of 180\u00b0. For a pentagon, which has five sides, the sum of all interior angles is:(5\u22122)\u00d7180\u2218=540\u2218(5 &#8211; 2) \\times 180^\\circ = 540^\\circ(5\u22122)\u00d7180\u2218=540\u2218<\/p>\n\n\n\n<p>We are given four of the five interior angles: two of them are right angles, meaning they measure 90\u00b0 each, and the other two are 100\u00b0 and 120\u00b0, respectively. By adding these known angles, we get:90\u2218+90\u2218+100\u2218+120\u2218=400\u221890^\\circ + 90^\\circ + 100^\\circ + 120^\\circ = 400^\\circ90\u2218+90\u2218+100\u2218+120\u2218=400\u2218<\/p>\n\n\n\n<p>Since the entire interior angle sum must be 540\u00b0, the measure of the missing, or fifth, angle must be the difference between 540\u00b0 and the total of the known angles:540\u2218\u2212400\u2218=140\u2218540^\\circ &#8211; 400^\\circ = 140^\\circ540\u2218\u2212400\u2218=140\u2218<\/p>\n\n\n\n<p>Therefore, the fifth angle in the pentagon must measure <strong>140 degrees<\/strong>. This ensures that the total of all five interior angles adds up correctly to 540\u00b0, satisfying the geometric property of a pentagon.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner9-273.jpeg\" alt=\"\" class=\"wp-image-232388\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>A pentagon has two right angles, a 100\u00b0 angle and a 120\u00b0 angle. What is the measure of its fifth angle The Correct Answer and Explanation is: A pentagon has 5 sides. The formula to find the sum of the interior angles of an n-sided polygon is:Sum&nbsp;of&nbsp;interior&nbsp;angles=(n\u22122)\u00d7180\u2218\\text{Sum of interior angles} = (n &#8211; 2) \\times [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-232387","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232387","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=232387"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232387\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=232387"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=232387"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=232387"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}