{"id":152,"date":"2022-04-13T08:29:38","date_gmt":"2022-04-13T08:29:38","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=152"},"modified":"2025-11-08T09:14:57","modified_gmt":"2025-11-08T09:14:57","slug":"i-4-review-interior-and-exterior-angles-of-polygons","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/i-4-review-interior-and-exterior-angles-of-polygons\/","title":{"rendered":"I.4 Review: interior and exterior 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>Review: interior and exterior 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\">\ud83e\udde9 <strong>What is a Polygon?<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A <strong>polygon<\/strong> is a closed figure made of <strong>straight line segments<\/strong>.<br>Examples: triangle, quadrilateral, pentagon, hexagon.<\/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\udfe1 <strong>Interior Angles<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Interior angles<\/strong> are the angles <strong>inside<\/strong> a polygon. \ud83c\udf1f<\/li>\n\n\n\n<li><strong>Sum of interior angles formula:<\/strong> <\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><strong>(n\u22122) \u00d7 180<sup>\u2218 <\/sup><\/strong><\/p>\n\n\n\n<p>\ud83d\udc49 Here, <strong>n = number of sides<\/strong><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u2728 Examples:<\/h4>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Polygon<\/th><th>n<\/th><th>Interior Sum<\/th><\/tr><\/thead><tbody><tr><td>Triangle<\/td><td>3<\/td><td>(3\u22122)\u00d7180\u00b0 = <strong>180\u00b0<\/strong><\/td><\/tr><tr><td>Quadrilateral<\/td><td>4<\/td><td>(4\u22122)\u00d7180\u00b0 = <strong>360\u00b0<\/strong><\/td><\/tr><tr><td>Pentagon<\/td><td>5<\/td><td>540\u00b0<\/td><\/tr><tr><td>Hexagon<\/td><td>6<\/td><td>720\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\">\ud83d\udd35 <strong>Exterior Angles<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Formed <strong>outside<\/strong> the polygon when a side is extended.<\/li>\n\n\n\n<li>Each exterior angle forms a <strong>linear pair<\/strong> with an interior angle.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">\ud83e\udde0 <strong>Most important rule:<\/strong><\/h4>\n\n\n\n<p class=\"has-text-align-center\"><strong>Sum&nbsp;of&nbsp;all&nbsp;exterior&nbsp;angles&nbsp;of&nbsp;any&nbsp;polygon=360<sup>\u2218<\/sup><\/strong><\/p>\n\n\n\n<p>\ud83d\udca1 This works for <strong>ALL<\/strong> polygons (regular or irregular)!<\/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\udfe3 <strong>Regular Polygons<\/strong><\/h3>\n\n\n\n<p>A <strong>regular polygon<\/strong> has <strong>all sides and angles equal<\/strong>.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>One interior angle (regular polygon):<\/strong> <\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><strong>(n\u22122)\u00d7180<sup>\u2218<\/sup> \/ n<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>One exterior angle (regular polygon):<\/strong> <\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><strong>360<sup>\u2218<\/sup> \/ n<\/strong><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\ud83c\udf1f Example:<\/h4>\n\n\n\n<p>Regular Hexagon \u2192 n = 6<br>Interior angle = 720\u00b0 \u00f7 6 = <strong>120\u00b0<\/strong><br>Exterior angle = 360\u00b0 \u00f7 6 = <strong>60\u00b0<\/strong><\/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\udd3b <strong>Interior + Exterior Angle Relationship<\/strong><\/h3>\n\n\n\n<p>For every vertex in a polygon: <\/p>\n\n\n\n<p>Interior&nbsp;angle+Exterior&nbsp;angle=180<sup>\u2218<\/sup><\/p>\n\n\n\n<p>(Because they form a <strong>linear pair<\/strong> \ud83d\udd01)<\/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\udde0 Quick Memory Tricks<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Concept<\/th><th>Trick<\/th><\/tr><\/thead><tbody><tr><td>Interior Sum<\/td><td>\u201c<strong>(Sides \u2212 2) \u00d7 180<\/strong>\u201d \ud83c\udfaf<\/td><\/tr><tr><td>Exterior Sum<\/td><td>\u201c<strong>Always 360\u00b0<\/strong>\u201d \ud83d\udd04<\/td><\/tr><tr><td>One exterior (regular)<\/td><td>360\u00b0 \u00f7 sides \ud83d\udccf<\/td><\/tr><tr><td>Int. + Ext.<\/td><td>Straight line = 180\u00b0 \u27a1\ufe0f<\/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\">\u2705 <strong>Fast Practice Check<\/strong><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Sum of interior angles of a 7-sided polygon?<br>\u2192 (7\u22122)\u00d7180 = <strong>900\u00b0<\/strong><\/li>\n\n\n\n<li>Exterior angle of a regular decagon (10 sides)?<br>\u2192 360\u00b0 \u00f7 10 = <strong>36\u00b0<\/strong><\/li>\n<\/ol>\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:#fbbdc4\"><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__83_-removebg-preview.png\" alt=\"\" class=\"wp-image-3515\" style=\"aspect-ratio:1;width:315px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__83_-removebg-preview.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__83_-removebg-preview-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__83_-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__83_-removebg-preview-1.png\" alt=\"\" class=\"wp-image-3516\" style=\"aspect-ratio:1;width:280px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__83_-removebg-preview-1.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__83_-removebg-preview-1-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__83_-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:#f5dac5\"><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__84_-removebg-preview.png\" alt=\"\" class=\"wp-image-3520\" style=\"width:171px;height:171px\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__84_-removebg-preview.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__84_-removebg-preview-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__84_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color has-large-font-size\" 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__84_-removebg-preview-1.png\" alt=\"\" class=\"wp-image-3521\" style=\"aspect-ratio:1;width:237px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__84_-removebg-preview-1.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__84_-removebg-preview-1-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__84_-removebg-preview-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>To&nbsp;find out how many triangles make up this polygon, pick a vertex and draw all the diagonals from that&nbsp;vertex.<\/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__85_-removebg-preview.png\" alt=\"\" class=\"wp-image-3522\" style=\"aspect-ratio:1;width:224px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__85_-removebg-preview.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__85_-removebg-preview-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__85_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>This&nbsp;polygon is made up of&nbsp;3&nbsp;triangles. Since the sum of the interior angle measures of each triangle is 180\u00b0, the sum of the interior angle measures of this polygon is&nbsp;3 . 180\u00b0 = 540\u00b0. <\/li>\n\n\n\n<li>Notice&nbsp;that this polygon has&nbsp;5&nbsp;sides and is made up of&nbsp;3&nbsp;triangles. In general, if a convex polygon has&nbsp;n&nbsp;sides it is made up of&nbsp;(n \u2013 2)&nbsp;triangles.<\/li>\n\n\n\n<li>In&nbsp;other words, the sum of the interior angle measures of a convex polygon with&nbsp;n&nbsp;sides is&nbsp;(n \u2013 2). 180\u00b0.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#fdebbe\"><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__86_-removebg-preview.png\" alt=\"\" class=\"wp-image-3525\" style=\"aspect-ratio:1;width:253px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__86_-removebg-preview.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__86_-removebg-preview-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__86_-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 exterior angle measures, one at each vertex, 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__86_-removebg-preview-1.png\" alt=\"\" class=\"wp-image-3526\" style=\"aspect-ratio:1;width:225px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__86_-removebg-preview-1.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__86_-removebg-preview-1-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__86_-removebg-preview-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>Since this polygon is convex, the sum of its exterior angle measures, one at each vertex, is 360\u00b0. The number of sides is not relevant.<\/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\/101544\/233\/908\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-48.png\" alt=\"\" class=\"wp-image-7822\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-48.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-48-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-48-150x150.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\/101544\/417\/616\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-57.png\" alt=\"\" class=\"wp-image-7823\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-57.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-57-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-57-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Review: interior and exterior angles of polygons key notes: \ud83e\udde9 What is a Polygon? \ud83d\udfe1 Interior Angles (n\u22122) \u00d7 180\u2218 \ud83d\udc49 Here, n = number of sides \u2728 Examples: Polygon n Interior Sum Triangle 3 (3\u22122)\u00d7180\u00b0 = 180\u00b0 Quadrilateral 4 (4\u22122)\u00d7180\u00b0 = 360\u00b0 Pentagon 5 540\u00b0 Hexagon 6 720\u00b0 \ud83d\udd35 Exterior Angles \ud83e\udde0 Most important<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/i-4-review-interior-and-exterior-angles-of-polygons\/\">Continue reading <span class=\"screen-reader-text\">&#8220;I.4 Review: interior and exterior 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-152","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/152","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=152"}],"version-history":[{"count":25,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/152\/revisions"}],"predecessor-version":[{"id":18235,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/152\/revisions\/18235"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=152"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}