What is the number of the side of the polygon if the sum of the measures of the angles of a convex polygon is 900?<\/p>\n\n\n\n
The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n The formula for the sum of the interior angles of a convex polygon is given by:<\/p>\n\n\n\n [ where ( n ) is the number of sides of the polygon.<\/p>\n\n\n\n Given that the sum of the interior angles of the polygon is 900 degrees, we can set up the equation:<\/p>\n\n\n\n [ Now, solve for ( n ):<\/p>\n\n\n\n [ [ [ [ Thus, the polygon has 7 sides.<\/p>\n\n\n\n To understand this, let’s break it down further. The sum of the interior angles of a polygon can be derived from the fact that any polygon can be divided into triangles. A triangle has a total interior angle sum of 180 degrees, and by dividing the polygon into triangles, we get the formula ( (n – 2) \\times 180 ) for the sum of the interior angles, where ( n ) is the number of sides.<\/p>\n\n\n\n For example, a quadrilateral (4-sided polygon) can be divided into 2 triangles, so the sum of the interior angles is ( (4 – 2) \\times 180 = 360 ) degrees. A pentagon (5-sided polygon) can be divided into 3 triangles, so the sum of the interior angles is ( (5 – 2) \\times 180 = 540 ) degrees, and so on.<\/p>\n\n\n\n In this problem, the sum of the interior angles is 900 degrees, which means the polygon must have 7 sides.<\/p>\n","protected":false},"excerpt":{"rendered":" What is the number of the side of the polygon if the sum of the measures of the angles of a convex polygon is 900? The correct answer and explanation is : The formula for the sum of the interior angles of a convex polygon is given by: [\\text{Sum of interior angles} = (n – […]<\/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-201370","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/201370","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=201370"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/201370\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=201370"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=201370"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=201370"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\\text{Sum of interior angles} = (n – 2) \\times 180
]<\/p>\n\n\n\n
(n – 2) \\times 180 = 900
]<\/p>\n\n\n\n\n
n – 2 = \\frac{900}{180}
]<\/p>\n\n\n\n
n – 2 = 5
]<\/p>\n\n\n\n\n
n = 5 + 2
]<\/p>\n\n\n\n
n = 7
]<\/p>\n\n\n\nExplanation:<\/h3>\n\n\n\n