{"id":153576,"date":"2022-03-25T22:34:37","date_gmt":"2022-03-25T17:04:37","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/interior-angles-of-a-polygon-formula-and-solved-examples\/"},"modified":"2024-05-06T14:26:29","modified_gmt":"2024-05-06T08:56:29","slug":"interior-angles-of-a-polygon-formula-and-solved-examples","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/interior-angles-of-a-polygon\/","title":{"rendered":"Interior Angles of a Polygon"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/interior-angles-of-a-polygon\/#Sum_of_Interior_Angles_of_a_Polygon_and_Formulas\" title=\"Sum of Interior Angles of a Polygon and Formulas\">Sum of Interior Angles of a Polygon and Formulas<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/interior-angles-of-a-polygon\/#Sum_of_Interior_Angles_of_a_Polygon_Formula\" title=\"Sum of Interior Angles of a Polygon Formula\">Sum of Interior Angles of a Polygon Formula<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/interior-angles-of-a-polygon\/#Sum_of_Interior_Angles_of_a_Regular_Polygon_and_Irregular_Polygon\" title=\"Sum of Interior Angles of a Regular Polygon and Irregular Polygon\">Sum of Interior Angles of a Regular Polygon and Irregular Polygon<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/interior-angles-of-a-polygon\/#A_Theorem_about_Interior_Angles\" title=\"A Theorem about Interior Angles\">A Theorem about Interior Angles<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/interior-angles-of-a-polygon\/#Sum_of_Interior_Angles_of_a_Polygon_with_Different_Number_of_Sides\" title=\"Sum of Interior Angles of a Polygon with Different Number of Sides:\">Sum of Interior Angles of a Polygon with Different Number of Sides:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/interior-angles-of-a-polygon\/#Sum_of_Interior_Angles_of_a_Polygon_Formula_Example_Problems\" title=\"Sum of Interior Angles of a Polygon Formula Example Problems:\">Sum of Interior Angles of a Polygon Formula Example Problems:<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Sum_of_Interior_Angles_of_a_Polygon_and_Formulas\"><\/span>Sum of Interior Angles of a Polygon and Formulas<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Interior Angles of a Polygon \u2013 Formula: The sum of the<a href=\"https:\/\/infinitylearn.com\/surge\/maths\/interior-angles-of-a-polygon\/\"> interior angles<\/a> of a polygon is the angle at the center of the polygon, multiplied by the number of sides. This is because the angle at the center of the polygon is 360 degrees, and each side is a fraction of that. For example, a pentagon has 5 sides, so the angle at the center is 360 degrees, and each side is 72 degrees. The sum of the interior angles of a polygon is always 360 degrees multiplied by the number of sides.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Sum_of_Interior_Angles_of_a_Polygon_Formula\"><\/span>Sum of Interior Angles of a Polygon Formula<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The sum of the interior angles of a polygon is equal to (n-2)*180, where n is the number of sides in the polygon. This formula is derived by taking the sum of the angles in a triangle (180), and then subtracting the angle between any two consecutive sides.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Sum_of_Interior_Angles_of_a_Regular_Polygon_and_Irregular_Polygon\"><\/span>Sum of Interior Angles of a Regular Polygon and Irregular Polygon<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The sum of the interior angles of a regular polygon is 360\u00b0. Therefore the sum of the interior angles of an irregular polygon is not a fixed number.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"A_Theorem_about_Interior_Angles\"><\/span>A Theorem about Interior Angles<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>If the sum of the angles inside a triangle is 180 degrees, then the largest angle is 180 degrees.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Sum_of_Interior_Angles_of_a_Polygon_with_Different_Number_of_Sides\"><\/span>Sum of Interior Angles of a Polygon with Different Number of Sides:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Therefore the sum of the interior angles of a polygon with different number of sides is 180 degrees.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Sum_of_Interior_Angles_of_a_Polygon_Formula_Example_Problems\"><\/span>Sum of Interior Angles of a Polygon Formula Example Problems:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>There are many different ways to find the sum of the interior angles of a polygon. One method is to use the formula:<\/p>\n<ul>\n<li>Sum of Interior Angles of a Polygon = (n-2)*180<\/li>\n<li>where &#8220;n&#8221; is the number of sides in the polygon.<\/li>\n<li>For example, if you have a hexagon with 6 sides, the sum of the interior angles is (6-2)*180 = 360 degrees.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Sum of Interior Angles of a Polygon and Formulas Interior Angles of a Polygon \u2013 Formula: The sum of the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Interior Angles of a Polygon","_yoast_wpseo_title":"Interior Angles of a Polygon \u2013 Formula and Solved Examples | IL","_yoast_wpseo_metadesc":"Learn about Interior Angles of a Polygon topic of Maths in details explained by subject experts on infinitylearn.com. 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