{"id":11230,"date":"2022-06-29T04:01:52","date_gmt":"2022-06-28T22:31:52","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11230"},"modified":"2022-06-29T04:01:56","modified_gmt":"2022-06-28T22:31:56","slug":"in-triangle-abc-anglec-3angleb-2anglea-angleb-find-the-three-angles-of-the-triangle","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/in-triangle-abc-anglec-3angleb-2anglea-angleb-find-the-three-angles-of-the-triangle\/","title":{"rendered":"In \\(\\triangle\\) ABC, \\(\\angle\\)C = 3\\(\\angle\\)B = 2(\\(\\angle\\)A + \\(\\angle\\)B). Find the three angles of the triangle."},"content":{"rendered":"

Solution :<\/h2>\n

Given,\u00a0 \\(\\angle\\)C = 2(\\(\\angle\\)A + \\(\\angle\\)B)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0…….(1)<\/p>\n

Adding 2\\(\\angle\\)C on both sides in equation (1), we get<\/p>\n

\\(\\angle\\)C + 2\\(\\angle\\)C = 2(\\(\\angle\\)A + \\(\\angle\\)B)\u00a0 + 2\\(\\angle\\)C<\/p>\n

\\(\\implies\\)\u00a0 3\\(\\angle\\)C = 2(\\(\\angle\\)A + \\(\\angle\\)B + \\(\\angle\\)C)<\/p>\n

Since, \\(\\angle\\)A + \\(\\angle\\)B + \\(\\angle\\)C = 180 degrees<\/p>\n

\\(\\implies\\)\u00a0 \\(\\angle\\)C = \\(2\\over 3\\) \\(\\times\\) 180 = 120<\/p>\n

Again, \\(\\angle\\)C = 3\\(\\angle\\)B<\/p>\n

120 = 3\\(\\angle\\)B\u00a0 \\(\\implies\\)\u00a0 \\(\\angle\\)B = 40<\/p>\n

But, \\(\\angle\\)A + \\(\\angle\\)B + \\(\\angle\\)C = 180<\/p>\n

\\(\\angle\\)A + 40 + 120 = 180<\/p>\n

\\(\\implies\\) \\(\\angle\\)A = 180 – 40 – 120 = 20<\/p>\n

Hence, \\(\\angle\\)A = 20, \\(\\angle\\)B = 40, \\(\\angle\\)C = 120<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Given,\u00a0 \\(\\angle\\)C = 2(\\(\\angle\\)A + \\(\\angle\\)B)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0…….(1) Adding 2\\(\\angle\\)C on both sides in equation (1), we get \\(\\angle\\)C + 2\\(\\angle\\)C = 2(\\(\\angle\\)A + \\(\\angle\\)B)\u00a0 + 2\\(\\angle\\)C \\(\\implies\\)\u00a0 3\\(\\angle\\)C = 2(\\(\\angle\\)A + \\(\\angle\\)B + \\(\\angle\\)C) Since, \\(\\angle\\)A + \\(\\angle\\)B + \\(\\angle\\)C = 180 degrees \\(\\implies\\)\u00a0 \\(\\angle\\)C = \\(2\\over 3\\) \\(\\times\\) …<\/p>\n

In \\(\\triangle\\) ABC, \\(\\angle\\)C = 3\\(\\angle\\)B = 2(\\(\\angle\\)A + \\(\\angle\\)B). Find the three angles of the triangle.<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[911,43],"tags":[],"yoast_head":"\nIn \\(\\triangle\\) ABC, \\(\\angle\\)C = 3\\(\\angle\\)B = 2(\\(\\angle\\)A + \\(\\angle\\)B). Find the three angles of the triangle. - Mathemerize<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/in-triangle-abc-anglec-3angleb-2anglea-angleb-find-the-three-angles-of-the-triangle\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"In \\(\\triangle\\) ABC, \\(\\angle\\)C = 3\\(\\angle\\)B = 2(\\(\\angle\\)A + \\(\\angle\\)B). Find the three angles of the triangle. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : Given,\u00a0 (angle)C = 2((angle)A + (angle)B)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0…….(1) Adding 2(angle)C on both sides in equation (1), we get (angle)C + 2(angle)C = 2((angle)A + (angle)B)\u00a0 + 2(angle)C (implies)\u00a0 3(angle)C = 2((angle)A + (angle)B + (angle)C) Since, (angle)A + (angle)B + (angle)C = 180 degrees (implies)\u00a0 (angle)C = (2over 3) (times) … In (triangle) ABC, (angle)C = 3(angle)B = 2((angle)A + (angle)B). Find the three angles of the triangle. 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Find the three angles of the triangle. - Mathemerize","og_description":"Solution : Given,\u00a0 (angle)C = 2((angle)A + (angle)B)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0…….(1) Adding 2(angle)C on both sides in equation (1), we get (angle)C + 2(angle)C = 2((angle)A + (angle)B)\u00a0 + 2(angle)C (implies)\u00a0 3(angle)C = 2((angle)A + (angle)B + (angle)C) Since, (angle)A + (angle)B + (angle)C = 180 degrees (implies)\u00a0 (angle)C = (2over 3) (times) … In (triangle) ABC, (angle)C = 3(angle)B = 2((angle)A + (angle)B). Find the three angles of the triangle. 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