{"id":247275,"date":"2025-07-07T15:39:06","date_gmt":"2025-07-07T15:39:06","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=247275"},"modified":"2025-07-07T15:39:09","modified_gmt":"2025-07-07T15:39:09","slug":"what-is-the-sum-of-the-interior-angle-of-a-regular-nonagon","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/07\/what-is-the-sum-of-the-interior-angle-of-a-regular-nonagon\/","title":{"rendered":"What is the sum of the interior angle of a regular nonagon"},"content":{"rendered":"\n<p>What is the sum of the interior angle of a regular nonagon? Select one: ? a. 1550\u00b0 ? b. 1440\u00b0 ? c. 1350\u00b0 ? d. 1260\u00b0<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-280.png\" alt=\"\" class=\"wp-image-247276\"\/><\/figure>\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>The correct answer is&nbsp;<strong>d. 1260\u00b0<\/strong>.<\/p>\n\n\n\n<p>To determine the sum of the interior angles of any polygon, you can use a standard formula. This formula is applicable whether the polygon is regular (having equal sides and angles) or irregular. The formula is:<\/p>\n\n\n\n<p>Sum of interior angles = (n &#8211; 2) \u00d7 180\u00b0<\/p>\n\n\n\n<p>In this formula, &#8216;n&#8217; represents the number of sides of the polygon.<\/p>\n\n\n\n<p>The question asks for the sum of the interior angles of a regular nonagon. A nonagon is a polygon with nine sides. Therefore, for this problem, n = 9.<\/p>\n\n\n\n<p>Now, we can substitute the value of &#8216;n&#8217; into the formula:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Start with the formula: Sum = (n &#8211; 2) \u00d7 180\u00b0<\/li>\n\n\n\n<li>Substitute n = 9: Sum = (9 &#8211; 2) \u00d7 180\u00b0<\/li>\n\n\n\n<li>Perform the subtraction inside the parentheses: Sum = 7 \u00d7 180\u00b0<\/li>\n\n\n\n<li>Multiply 7 by 180 to find the final sum: Sum = 1260\u00b0<\/li>\n<\/ol>\n\n\n\n<p>The logic behind this formula is that any polygon can be divided into a number of triangles by drawing diagonals from a single vertex. The number of triangles you can create is always two less than the number of sides (n &#8211; 2). Since the sum of angles in any triangle is always 180\u00b0, you can find the total sum of the polygon&#8217;s angles by multiplying the number of triangles by 180\u00b0. For a nine-sided nonagon, you can create 7 triangles, leading to the calculation 7 \u00d7 180\u00b0.<\/p>\n\n\n\n<p>Comparing our calculated result of 1260\u00b0 with the given options:<br>a. 1550\u00b0<br>b. 1440\u00b0<br>c. 1350\u00b0<br>d. 1260\u00b0<\/p>\n\n\n\n<p>The result matches option d, confirming it is the correct answer.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-997.jpeg\" alt=\"\" class=\"wp-image-247277\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>What is the sum of the interior angle of a regular nonagon? Select one: ? a. 1550\u00b0 ? b. 1440\u00b0 ? c. 1350\u00b0 ? d. 1260\u00b0 The Correct Answer and Explanation is: The correct answer is&nbsp;d. 1260\u00b0. To determine the sum of the interior angles of any polygon, you can use a standard formula. This [&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-247275","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/247275","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=247275"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/247275\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=247275"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=247275"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=247275"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}