{"id":148,"date":"2022-04-13T08:28:58","date_gmt":"2022-04-13T08:28:58","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=148"},"modified":"2025-11-08T08:48:35","modified_gmt":"2025-11-08T08:48:35","slug":"i-2-interior-angles-of-polygons","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/i-2-interior-angles-of-polygons\/","title":{"rendered":"I.2 Interior angles of polygons"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Interior angles of polygons<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b\">key notes :<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udd37 <strong>What is an Interior Angle?<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>An <strong>interior angle<\/strong> is the <strong>angle formed inside a polygon<\/strong> at each vertex \u2728.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\u2705 <strong>Sum of Interior Angles Formula<\/strong><\/h3>\n\n\n\n<p>For any polygon with <strong>n sides<\/strong>: <\/p>\n\n\n\n<p>Sum&nbsp;of&nbsp;Interior&nbsp;Angles = (n\u22122) \u00d7 180\u00b0<\/p>\n\n\n\n<p>\ud83d\udccd Example: For a pentagon (5 sides)<br>Sum = (5 \u2212 2) \u00d7 180\u00b0 = <strong>540\u00b0<\/strong> \ud83d\udd25<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udcd0 <strong>Interior Angle of a Regular Polygon<\/strong><\/h3>\n\n\n\n<p>A <strong>regular polygon<\/strong> has <strong>all sides and angles equal<\/strong> \ud83d\udca0. <\/p>\n\n\n\n<p>Each&nbsp;Interior&nbsp;Angle = (n\u22122)\u00d7180\u00b0 \/ n<\/p>\n\n\n\n<p>\ud83d\udccd Example: Regular hexagon (6 sides)<br>Each angle = (6\u22122)\u00d7180\u00b0 \/ 6 = 120\u00b0 \ud83c\udf1f<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83e\uddee <strong>Quick Reference Table<\/strong><\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Polygon<\/th><th>Sides (n)<\/th><th>Sum of Interior Angles<\/th><th>Each Angle (Regular)<\/th><\/tr><\/thead><tbody><tr><td>Triangle \ud83d\udd3a<\/td><td>3<\/td><td>180\u00b0<\/td><td>60\u00b0<\/td><\/tr><tr><td>Quadrilateral \u2b1c<\/td><td>4<\/td><td>360\u00b0<\/td><td>90\u00b0<\/td><\/tr><tr><td>Pentagon \u2b50<\/td><td>5<\/td><td>540\u00b0<\/td><td>108\u00b0<\/td><\/tr><tr><td>Hexagon \ud83d\udd37<\/td><td>6<\/td><td>720\u00b0<\/td><td>120\u00b0<\/td><\/tr><tr><td>Heptagon \ud83c\udf08<\/td><td>7<\/td><td>900\u00b0<\/td><td>~128.57\u00b0<\/td><\/tr><tr><td>Octagon \ud83d\uded1<\/td><td>8<\/td><td>1080\u00b0<\/td><td>135\u00b0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83e\udde0 <strong>Why (n \u2212 2)?<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Any polygon can be divided into <strong>(n \u2212 2) triangles<\/strong> \ud83d\udd3a\ud83d\udd3a\ud83d\udd3a<\/li>\n\n\n\n<li>Each triangle = <strong>180\u00b0<\/strong><\/li>\n\n\n\n<li>So multiply triangles \u00d7 180\u00b0 \u2705<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udea6 Important Tips to Remember<\/h3>\n\n\n\n<p>\ud83d\udca1 Interior angles <strong>increase<\/strong> as the number of sides increases.<br>\ud83d\udca1 Regular polygons have <strong>equal<\/strong> interior and exterior angles.<br>\ud83d\udca1 Exterior angle of a regular polygon = <strong>360\u00b0 \u00f7 n<\/strong> \ud83d\udd01<br>\ud83d\udca1 Interior + Exterior angle at a vertex = <strong>180\u00b0<\/strong> (Linear pair) \ud83d\udccf<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83c\udfc1 Summary<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Interior angle \u2192 inside the polygon \ud83c\udfe0<\/li>\n\n\n\n<li>Sum of interior angles \u2192 (n\u22122) \u00d7 180\u00b0<\/li>\n\n\n\n<li>Each angle (regular polygon) \u2192 (n\u22122) \u00d7 180\u00b0\/n<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#9fc5f8\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>\u2708\ufe0f The&nbsp;diagram shows a convex&nbsp;polygon.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__77_-removebg-preview.png\" alt=\"\" class=\"wp-image-3487\" style=\"width:238px;height:238px\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__77_-removebg-preview.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__77_-removebg-preview-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__77_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>\u2708\ufe0f  What&nbsp;is the sum of the interior angle measures of this&nbsp;polygon?<\/strong><\/p>\n\n\n\n<p>______ \u00b0<\/p>\n<\/div><\/div>\n\n\n\n<p>Look&nbsp;at this convex&nbsp;polygon.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__77_-removebg-preview-1.png\" alt=\"\" class=\"wp-image-3488\" style=\"aspect-ratio:1;width:308px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__77_-removebg-preview-1.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__77_-removebg-preview-1-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__77_-removebg-preview-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>This polygon is a triangle, so the sum of the interior angles is 180\u00b0.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#ffedd0\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>\u2708\ufe0f The&nbsp;diagram shows a convex&nbsp;polygon.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__78_-removebg-preview.png\" alt=\"\" class=\"wp-image-3491\" style=\"width:196px;height:196px\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__78_-removebg-preview.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__78_-removebg-preview-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__78_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>\u2708\ufe0f What&nbsp;is the sum of the interior angle measures of this&nbsp;polygon?<\/strong><\/p>\n\n\n\n<p>________\u00b0<\/p>\n<\/div><\/div>\n\n\n\n<p>The&nbsp;sum of the interior angle measures of a triangle is&nbsp;180\u00b0.<\/p>\n\n\n\n<p>Look&nbsp;at this convex&nbsp;polygon.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__78_-removebg-preview-1.png\" alt=\"\" class=\"wp-image-3492\" style=\"aspect-ratio:1;width:258px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__78_-removebg-preview-1.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__78_-removebg-preview-1-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__78_-removebg-preview-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>This polygon is a triangle, so the sum of the interior angles is 180\u00b0.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#bdc4fc\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>\u2708\ufe0f The&nbsp;diagram shows a convex&nbsp;polygon.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__79_-removebg-preview.png\" alt=\"\" class=\"wp-image-3495\" style=\"aspect-ratio:1;width:271px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__79_-removebg-preview.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__79_-removebg-preview-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__79_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>\u2708\ufe0f What&nbsp;is the sum of the interior angle measures of this&nbsp;polygon?<\/strong><\/p>\n\n\n\n<p>______\u00b0<\/p>\n<\/div><\/div>\n\n\n\n<p>Look&nbsp;at this convex&nbsp;polygon.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__79_-removebg-preview-1.png\" alt=\"\" class=\"wp-image-3496\" style=\"aspect-ratio:1;width:235px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__79_-removebg-preview-1.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__79_-removebg-preview-1-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__79_-removebg-preview-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>This polygon is a triangle, so the sum of the interior angles is 180\u00b0.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">let&#8217;s practice! \ud83d\udd8a\ufe0f<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/40725\/596\/570\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-50.png\" alt=\"\" class=\"wp-image-7829\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-50.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-50-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-50-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/82478\/109\/323\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-59.png\" alt=\"\" class=\"wp-image-7830\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-59.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-59-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-59-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Interior angles of polygons key notes : \ud83d\udd37 What is an Interior Angle? \u2705 Sum of Interior Angles Formula For any polygon with n sides: Sum&nbsp;of&nbsp;Interior&nbsp;Angles = (n\u22122) \u00d7 180\u00b0 \ud83d\udccd Example: For a pentagon (5 sides)Sum = (5 \u2212 2) \u00d7 180\u00b0 = 540\u00b0 \ud83d\udd25 \ud83d\udcd0 Interior Angle of a Regular Polygon A regular<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/i-2-interior-angles-of-polygons\/\">Continue reading <span class=\"screen-reader-text\">&#8220;I.2 Interior angles of polygons&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-148","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/148","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=148"}],"version-history":[{"count":24,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/148\/revisions"}],"predecessor-version":[{"id":18231,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/148\/revisions\/18231"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=148"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}