- \n
- Triangle A (Main Roof):<\/strong>\u00a0The missing angle is\u00a0100\u00b0<\/strong>.<\/li>\n\n\n\n
- Triangle B (Dormer Window):<\/strong>\u00a0The missing angle is\u00a030\u00b0<\/strong>.<\/li>\n\n\n\n
- Triangle C (Gable Decoration):<\/strong>\u00a0The missing angle is\u00a055\u00b0<\/strong>.<\/li>\n<\/ul>\n\n\n\n
\n\n\n\nExplanation: The Angle Sum Property of Triangles<\/strong><\/h3>\n\n\n\n
To find the missing angles in the house diagram, we use a fundamental rule of geometry: The sum of the interior angles in any triangle always equals 180 degrees.<\/strong> This principle is the key to solving for any unknown angle when the other two are known. Let\u2019s break down each triangle from the worksheet.<\/p>\n\n\n\n
Triangle A: The Main Roof<\/strong><\/h4>\n\n\n\n
- \n
- Given Information:<\/strong>\u00a0This is an isosceles triangle, identified by the two equal base angles of 40\u00b0 each.<\/li>\n\n\n\n
- Principle:<\/strong>\u00a0We apply the 180\u00b0 rule. We know two angles, so we can set up an equation to find the third angle, which we’ll call\u00a0x<\/em>.<\/li>\n\n\n\n
- Calculation:<\/strong>
Angle 1 + Angle 2 + Angle\u00a0x<\/em>\u00a0= 180\u00b0
40\u00b0 + 40\u00b0 +\u00a0x<\/em>\u00a0= 180\u00b0
80\u00b0 +\u00a0x<\/em>\u00a0= 180\u00b0
To isolate\u00a0x<\/em>, we subtract 80\u00b0 from both sides:
x<\/em>\u00a0= 180\u00b0 – 80\u00b0
x<\/em>\u00a0= 100\u00b0<\/li>\n\n\n\n- Answer:<\/strong>\u00a0The missing angle at the peak of the roof is\u00a0100\u00b0<\/strong>.<\/li>\n<\/ul>\n\n\n\n
Triangle B: The Dormer Window<\/strong><\/h4>\n\n\n\n
- \n
- Given Information:<\/strong>\u00a0This is a right-angled triangle, indicated by the square symbol, which means one angle is exactly 90\u00b0. The other given angle is 60\u00b0.<\/li>\n\n\n\n
- Principle:<\/strong>\u00a0Even in a specialized triangle like a right-angled one, the sum of its angles is still 180\u00b0.<\/li>\n\n\n\n
- Calculation:<\/strong>
Angle 1 + Angle 2 + Angle\u00a0y<\/em>\u00a0= 180\u00b0
90\u00b0 + 60\u00b0 +\u00a0y<\/em>\u00a0= 180\u00b0
150\u00b0 +\u00a0y<\/em>\u00a0= 180\u00b0
To find\u00a0y<\/em>, we subtract 150\u00b0 from 180\u00b0:
y<\/em>\u00a0= 180\u00b0 – 150\u00b0
y<\/em>\u00a0= 30\u00b0<\/li>\n\n\n\n- Answer:<\/strong>\u00a0The missing acute angle in the dormer window is\u00a030\u00b0<\/strong>.<\/li>\n<\/ul>\n\n\n\n
Triangle C: The Gable Decoration<\/strong><\/h4>\n\n\n\n
- \n
- Given Information:<\/strong>\u00a0This scalene triangle has two different angles provided: 75\u00b0 and 50\u00b0.<\/li>\n\n\n\n
- Principle:<\/strong>\u00a0We once again use the angle sum property.<\/li>\n\n\n\n
- Calculation:<\/strong>
Angle 1 + Angle 2 + Angle\u00a0z<\/em>\u00a0= 180\u00b0
75\u00b0 + 50\u00b0 +\u00a0z<\/em>\u00a0= 180\u00b0
125\u00b0 +\u00a0z<\/em>\u00a0= 180\u00b0
To solve for\u00a0z<\/em>, subtract 125\u00b0 from 180\u00b0:
z<\/em>\u00a0= 180\u00b0 – 125\u00b0
z<\/em>\u00a0= 55\u00b0<\/li>\n\n\n\n- Answer:<\/strong>\u00a0The third angle in the gable decoration is\u00a055\u00b0<\/strong><\/li>\n<\/ul>\n\n\n\n
![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner4-889.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"finding missing angles in triangles worksheet answers house The Correct Answer and Explanation is: Worksheet Answers: The Geometry House Explanation: The Angle Sum Property of Triangles To find the missing angles in the house diagram, we use a fundamental rule of geometry: The sum of the interior angles in any triangle always equals 180 degrees. This principle […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","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":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-231387","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/231387","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=231387"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/231387\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=231387"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=231387"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=231387"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- Principle:<\/strong>\u00a0We once again use the angle sum property.<\/li>\n\n\n\n
- Principle:<\/strong>\u00a0Even in a specialized triangle like a right-angled one, the sum of its angles is still 180\u00b0.<\/li>\n\n\n\n
- Principle:<\/strong>\u00a0We apply the 180\u00b0 rule. We know two angles, so we can set up an equation to find the third angle, which we’ll call\u00a0x<\/em>.<\/li>\n\n\n\n
- Triangle B (Dormer Window):<\/strong>\u00a0The missing angle is\u00a030\u00b0<\/strong>.<\/li>\n\n\n\n