A rhombus. Angle a is 100 degrees. Angle c is opposite to angle a. Angles b and d are opposite to each other. In rhombus abcd, the measure of angle a is 100\u00b0. Find the measure of the other angles.<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n In a rhombus, opposite angles are equal, and the sum of adjacent angles is always 180\u00b0 because a rhombus is a type of parallelogram. Here, we have rhombus ABCD, where angle A is given as 100\u00b0. Let’s analyze the measures of the other angles in this rhombus.<\/p>\n\n\n\n The properties of a rhombus provide a straightforward way to find unknown angles once one angle is known. A rhombus is a quadrilateral with all sides of equal length and opposite angles that are equal. Additionally, adjacent angles in a rhombus are supplementary, which means they add up to 180\u00b0. Knowing this, we determined that since angle A is 100\u00b0, angle C (opposite angle) is also 100\u00b0. Then, using the property of supplementary angles, we calculated angle B by subtracting angle A from 180\u00b0, giving us 80\u00b0 for both angle B and its opposite, angle D. This consistency in angle measures reflects the symmetry of a rhombus, where opposite angles are equal, and adjacent angles always add to 180\u00b0.<\/p>\n","protected":false},"excerpt":{"rendered":" A rhombus. Angle a is 100 degrees. Angle c is opposite to angle a. Angles b and d are opposite to each other. In rhombus abcd, the measure of angle a is 100\u00b0. Find the measure of the other angles. The Correct Answer and Explanation is: In a rhombus, opposite angles are equal, and the […]<\/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-165133","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/165133","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=165133"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/165133\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=165133"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=165133"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=165133"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Solution:<\/h3>\n\n\n\n
\n
\\text{angle A} + \\text{angle B} = 180\u00b0
]
[
100\u00b0 + \\text{angle B} = 180\u00b0
]
[
\\text{angle B} = 180\u00b0 – 100\u00b0 = 80\u00b0
]<\/li>\n\n\n\nSummary of Angle Measures:<\/h3>\n\n\n\n
\n
Explanation:<\/h3>\n\n\n\n