{"id":205271,"date":"2025-03-24T09:49:52","date_gmt":"2025-03-24T09:49:52","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=205271"},"modified":"2025-03-24T09:49:56","modified_gmt":"2025-03-24T09:49:56","slug":"chelsea-drew-a-16-sided-polygon","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/24\/chelsea-drew-a-16-sided-polygon\/","title":{"rendered":"Chelsea drew a 16-sided polygon"},"content":{"rendered":"\n<p>Chelsea drew a 16-sided polygon.<\/p>\n\n\n\n<p>What is the sum of the interior angles of the 16-sided polygon?<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/03\/image-1254.png\" alt=\"\" class=\"wp-image-205272\"\/><\/figure>\n\n\n\n<p>To determine the sum of the interior angles of a 16-sided polygon, we can apply a standard formula used for any polygon with &#8216;n&#8217; sides:<\/p>\n\n\n\n<p><strong>Sum of Interior Angles = (n \u2013 2) \u00d7 180\u00b0<\/strong><\/p>\n\n\n\n<p>In this case, the polygon has 16 sides, so:<\/p>\n\n\n\n<p><strong>Sum of Interior Angles = (16 \u2013 2) \u00d7 180\u00b0 = 14 \u00d7 180\u00b0 = 2,520\u00b0<\/strong><\/p>\n\n\n\n<p>This means that the sum of all interior angles of a 16-sided polygon is 2,520 degrees.<\/p>\n\n\n\n<p><strong>Explanation:<\/strong><\/p>\n\n\n\n<p>A polygon is a two-dimensional geometric figure with straight sides that are fully closed. The number of sides (n) significantly influences the sum of its interior angles. To understand why the formula (n \u2013 2) \u00d7 180\u00b0 works, consider the following:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Triangulation Method:<\/strong> Any polygon can be divided into triangles by drawing diagonals from one vertex to all other non-adjacent vertices. Each triangle has interior angles summing to 180\u00b0. The number of triangles formed in an n-sided polygon is (n \u2013 2). Therefore, the total sum of interior angles is (n \u2013 2) \u00d7 180\u00b0.<\/li>\n\n\n\n<li><strong>Example with a Triangle (n = 3):<\/strong> Dividing a triangle into (3 \u2013 2) = 1 triangle gives 1 \u00d7 180\u00b0 = 180\u00b0, which matches the sum of interior angles of a triangle.<\/li>\n\n\n\n<li><strong>Example with a Quadrilateral (n = 4):<\/strong> Dividing a quadrilateral into (4 \u2013 2) = 2 triangles gives 2 \u00d7 180\u00b0 = 360\u00b0, which matches the sum of interior angles of a quadrilateral.<\/li>\n<\/ul>\n\n\n\n<p>Applying this reasoning to a 16-sided polygon:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Number of Triangles:<\/strong> (16 \u2013 2) = 14 triangles.<\/li>\n\n\n\n<li><strong>Sum of Interior Angles:<\/strong> 14 \u00d7 180\u00b0 = 2,520\u00b0.<\/li>\n<\/ul>\n\n\n\n<p>This consistent method allows us to calculate the sum of interior angles for any polygon, regardless of whether it&#8217;s regular (all sides and angles equal) or irregular.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Chelsea drew a 16-sided polygon. What is the sum of the interior angles of the 16-sided polygon? The correct answer and explanation is : To determine the sum of the interior angles of a 16-sided polygon, we can apply a standard formula used for any polygon with &#8216;n&#8217; sides: Sum of Interior Angles = (n [&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-205271","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/205271","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=205271"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/205271\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=205271"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=205271"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=205271"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}