{"id":104,"date":"2022-04-13T08:21:09","date_gmt":"2022-04-13T08:21:09","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=104"},"modified":"2025-10-24T04:39:36","modified_gmt":"2025-10-24T04:39:36","slug":"g-2-triangle-angle-sum-property","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/g-2-triangle-angle-sum-property\/","title":{"rendered":"G.2 Triangle angle-sum property"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Triangle angle-sum property<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-a7babd01df25c034f9938b577dbd6ba0\" style=\"color:#74008b;text-transform:capitalize\">key notes :<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-f2b6c3eb5fe2a989813ba219a46e6f81\" style=\"color:#000060\">1\ufe0f\u20e3 <strong>Definition:<\/strong><\/p>\n\n\n\n<p>\ud83d\udc49 The <strong>angle-sum property<\/strong> of a triangle states that the <strong>sum of the three interior angles<\/strong> of a triangle is always <strong>180\u00b0<\/strong>. \ud83c\udfaf <\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>\u2220A&nbsp;+&nbsp;\u2220B&nbsp;+&nbsp;\u2220C&nbsp;=&nbsp;180\u00b0<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-804b258472360c7a419104a870c0fd0b\" style=\"color:#000060\">2\ufe0f\u20e3 <strong>\ud83d\udca1 Important Concept:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>This rule applies to <strong>all types of triangles<\/strong> \u2014 \ud83d\udd39 <strong>acute<\/strong>, \ud83d\udd38 <strong>right<\/strong>, and \ud83d\udd3a <strong>obtuse<\/strong> triangles.<\/li>\n\n\n\n<li>Even if the sides or angles change, the <strong>total sum of interior angles<\/strong> remains <strong>constant<\/strong> (180\u00b0)! \ud83d\udd25<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-14df457536148dbdf1e0e892f1ea4487\" style=\"color:#000060\">3\ufe0f\u20e3 <strong>\ud83d\udcd0 Examples:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Example 1: If \u2220A = 60\u00b0, \u2220B = 70\u00b0, find \u2220C.<br>\u270f\ufe0f \u2220C = 180\u00b0 \u2013 (60\u00b0 + 70\u00b0) = <strong>50\u00b0<\/strong> \u2705<\/li>\n\n\n\n<li>Example 2: If \u2220A = 90\u00b0, \u2220B = 45\u00b0, find \u2220C.<br>\u270f\ufe0f \u2220C = 180\u00b0 \u2013 (90\u00b0 + 45\u00b0) = <strong>45\u00b0<\/strong> \u2705<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-da51b6c28e833aba114b375347b82b36\" style=\"color:#000060\">4\ufe0f\u20e3 <strong>\ud83c\udf1f For Exterior Angles:<\/strong><\/p>\n\n\n\n<p>\ud83d\udc49 The <strong>exterior angle<\/strong> of a triangle equals the <strong>sum of the two opposite interior angles<\/strong>. <\/p>\n\n\n\n<p>Exterior&nbsp;angle&nbsp;=&nbsp;\u22201&nbsp;+&nbsp;\u22202<\/p>\n\n\n\n<p>\ud83e\udde0 Example: If one exterior angle = 120\u00b0, and one interior opposite angle = 50\u00b0,<br>then the other opposite angle = 120\u00b0 \u2013 50\u00b0 = <strong>70\u00b0<\/strong> \u2728<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-d28b62a47687594dcebc1f4250f4f6f5\" style=\"color:#000060\">5\ufe0f\u20e3 <strong>\ud83e\udde9 Real-Life Connection:<\/strong><\/p>\n\n\n\n<p>Triangles are everywhere! \ud83c\udfe0<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Roofs, signboards, and bridges use triangular shapes because they\u2019re <strong>strong and stable<\/strong> \u2014 and this property helps engineers calculate angles perfectly! \ud83d\udcaa\ud83d\udccf<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-4f099435b42cc23274ddaf698040f23e\" style=\"color:#000060\">6\ufe0f\u20e3 <strong>\ud83c\udfaf Key Takeaways:<\/strong><\/p>\n\n\n\n<p>\u2705 The sum of interior angles of a triangle = <strong>180\u00b0<\/strong><br>\u2705 The exterior angle = <strong>sum of two opposite interior angles<\/strong><br>\u2705 Applies to <strong>all types<\/strong> of triangles<br>\u2705 Used in <strong>geometry, design, and construction<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-1e0fa2ca4b503eae2c22a8d02f78fb04\" style=\"color:#000060\">\ud83d\udcac <strong>Mnemonic to Remember:<\/strong><\/p>\n\n\n\n<p>\ud83c\udf00 \u201c<strong>All Triangles Add Up to 180!<\/strong>\u201d \ud83c\udf00<\/p>\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-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-84e01f08994b7ae7647b3c9132bb6927\" style=\"background-color:#e2c4fb\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-c0fd3f3c23106a7e17e8c4fd53155cae\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>The&nbsp;diagram shows a&nbsp;triangle.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled-design-3-1.png\" alt=\"\" class=\"wp-image-8458\" style=\"width:386px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled-design-3-1.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled-design-3-1-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled-design-3-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>What is the value of c?<\/strong><\/p>\n\n\n\n<p>c =_____\u00b0<\/p>\n<\/div><\/div>\n\n\n\n<p>First,&nbsp;look at the interior angle measures in the&nbsp;triangle.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design__3_-removebg-preview.png\" alt=\"\" class=\"wp-image-8459\" style=\"width:384px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design__3_-removebg-preview.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design__3_-removebg-preview-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design__3_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>Set the sum of the interior angle measures of the triangle equal to 180\u00b0. Solve for c.<\/p>\n\n\n\n<p>c+84\u00b0+58\u00b0 = 180\u00b0<\/p>\n\n\n\n<p>c+142\u00b0 = 180\u00b0        Combine like terms<\/p>\n\n\n\n<p>c = 38\u00b0               Subtract 142\u00b0 from both sides<\/p>\n\n\n\n<p>So, c=38\u00b0.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-8d47d4cc7341ad9f5a754eaf8768323b\" style=\"background-color:#cdf9b0\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-fec660d800c0a41ed781be78915e3069\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>The&nbsp;diagram shows a&nbsp;triangle.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled-design-4.png\" alt=\"\" class=\"wp-image-8462\" style=\"width:406px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled-design-4.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled-design-4-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled-design-4-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>What is the value of b?<\/strong><\/p>\n\n\n\n<p>b = ____\u00b0<\/p>\n<\/div><\/div>\n\n\n\n<p>First,&nbsp;look at the interior angle measures in the&nbsp;triangle.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design__4_-removebg-preview-1.png\" alt=\"\" class=\"wp-image-8463\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design__4_-removebg-preview-1.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design__4_-removebg-preview-1-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design__4_-removebg-preview-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>Set the sum of the interior angle measures of the triangle equal to 180\u00b0. Solve for b.<\/p>\n\n\n\n<p>67\u00b0+32\u00b0+b = 180\u00b0<\/p>\n\n\n\n<p>b+99\u00b0 = 180\u00b0          Combine like terms<\/p>\n\n\n\n<p>b = 81\u00b0               Subtract 99\u00b0 from both sides<\/p>\n\n\n\n<p>So, b=81\u00b0.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-720e79c0ea0e159d73ff516ec33102da\" style=\"background-color:#bed1f6\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-09d839b8af8be940514afd483d39c8c4\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>The&nbsp;diagram shows a&nbsp;triangle.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled-design-5-1.png\" alt=\"\" class=\"wp-image-8464\" style=\"width:350px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled-design-5-1.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled-design-5-1-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled-design-5-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>What is the value of b?<\/strong><\/p>\n\n\n\n<p>b = ____\u00b0<\/p>\n<\/div><\/div>\n\n\n\n<p>First,&nbsp;look at the interior angle measures in the&nbsp;triangle.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design__5_-removebg-preview-1.png\" alt=\"\" class=\"wp-image-8465\" style=\"width:410px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design__5_-removebg-preview-1.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design__5_-removebg-preview-1-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design__5_-removebg-preview-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>Set the sum of the interior angle measures of the triangle equal to 180\u00b0. Solve for b.<\/p>\n\n\n\n<p>b+98\u00b0+40\u00b0 = 180\u00b0<\/p>\n\n\n\n<p>b+138\u00b0 = 180\u00b0            Combine like terms<\/p>\n\n\n\n<p>b= 42\u00b0                   Subtract 138\u00b0 from both sides<\/p>\n\n\n\n<p>So, b=42\u00b0.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-columns are-vertically-aligned-center has-background is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\" style=\"background-color:#ffef76\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/09\/Pink_Modern_Minimalist_Microphone_Talk_Podcast_Cover-removebg-preview-8.png\" alt=\"\" class=\"wp-image-10120\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/09\/Pink_Modern_Minimalist_Microphone_Talk_Podcast_Cover-removebg-preview-8.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/09\/Pink_Modern_Minimalist_Microphone_Talk_Podcast_Cover-removebg-preview-8-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/09\/Pink_Modern_Minimalist_Microphone_Talk_Podcast_Cover-removebg-preview-8-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/09\/1695719675725lq7d2lni-voicemaker.in-speech.mp3\"><\/audio><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\"><strong>Let&#8217;s practice!<\/strong><\/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\/81292\/795\/268\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-36.png\" alt=\"\" class=\"wp-image-7767\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-36.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-36-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-36-150x150.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\/81095\/825\/441\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-41.png\" alt=\"\" class=\"wp-image-7768\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-41.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-41-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-41-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Triangle angle-sum property key notes : 1\ufe0f\u20e3 Definition: \ud83d\udc49 The angle-sum property of a triangle states that the sum of the three interior angles of a triangle is always 180\u00b0. \ud83c\udfaf \u2220A&nbsp;+&nbsp;\u2220B&nbsp;+&nbsp;\u2220C&nbsp;=&nbsp;180\u00b0 2\ufe0f\u20e3 \ud83d\udca1 Important Concept: 3\ufe0f\u20e3 \ud83d\udcd0 Examples: 4\ufe0f\u20e3 \ud83c\udf1f For Exterior Angles: \ud83d\udc49 The exterior angle of a triangle equals the sum of<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/g-2-triangle-angle-sum-property\/\">Continue reading <span class=\"screen-reader-text\">&#8220;G.2 Triangle angle-sum property&#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-104","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/104","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=104"}],"version-history":[{"count":24,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/104\/revisions"}],"predecessor-version":[{"id":18108,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/104\/revisions\/18108"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=104"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}