{"id":220997,"date":"2025-05-29T05:33:29","date_gmt":"2025-05-29T05:33:29","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=220997"},"modified":"2025-05-29T05:33:31","modified_gmt":"2025-05-29T05:33:31","slug":"find-the-measures-of-the-numbered-angles-in-each-rectangle","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/29\/find-the-measures-of-the-numbered-angles-in-each-rectangle\/","title":{"rendered":"Find the measures of the numbered angles in each rectangle."},"content":{"rendered":"\n<p>Find the measures of the numbered angles in each rectangle. 7. 21 61\u00b0 4. 3. 5. Find the measures of the numbered angles in each rectangle. Angle 1 Angle 2 Angle 3 Angle 4 Angle 5\u00a0<img decoding=\"async\" src=\"https:\/\/files.transtutors.com\/cdn\/qimg\/4c484e43-d9f7-411f-9bc3-243ebde90435.png\">\u00a01. A rectangle is a parallelogram. sometimes A rhombus is a square. 2. 3. A parallelogram is a rhombus. never 4. A rhombus is a rectangle. never 5. A square is a rhombus. always 6. A rectangle is a quadrilateral always Find the measures of the numbered angles in each rectangle. 7. 5 8. 61 3 4 2 4 1 2 m2 m23 m24 m25 m21= m42 =<br><\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is<\/mark><\/strong>:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Given:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The shape is a <strong>rectangle<\/strong>.<\/li>\n\n\n\n<li>One of the angles (Angle 4) is given as <strong>61\u00b0<\/strong>.<\/li>\n\n\n\n<li>The rectangle has a diagonal line that splits it into two right triangles.<\/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\">Key Geometry Concepts:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>All interior angles of a rectangle are 90\u00b0.<\/strong><\/li>\n\n\n\n<li><strong>Diagonals of a rectangle are congruent<\/strong> and divide the rectangle into <strong>two congruent right triangles.<\/strong><\/li>\n\n\n\n<li>The <strong>sum of angles in a triangle<\/strong> is <strong>180\u00b0.<\/strong><\/li>\n\n\n\n<li>In a triangle, if one angle is known, the other two can be found using the 180\u00b0 total.<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Solving the Angles:<\/h3>\n\n\n\n<p>We are told \u22204 = <strong>61\u00b0<\/strong>.<\/p>\n\n\n\n<p>Since this triangle lies within a right triangle (half the rectangle), one of the angles (Angle 3) must be <strong>90\u00b0<\/strong>, because all corners of a rectangle are 90\u00b0.<\/p>\n\n\n\n<p>Let\u2019s now analyze triangle formed by angles \u22203, \u22204, and \u22205:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u22203 = 90\u00b0 (corner of rectangle)<\/li>\n\n\n\n<li>\u22204 = 61\u00b0 (given)<\/li>\n\n\n\n<li>\u22205 = 180\u00b0 &#8211; (90\u00b0 + 61\u00b0) = <strong>29\u00b0<\/strong><\/li>\n<\/ul>\n\n\n\n<p>So:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u22205 = 29\u00b0<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Now let\u2019s look at the triangle on the other side (containing angles 1 and 2):<\/p>\n\n\n\n<p>Since diagonals in a rectangle are congruent and opposite triangles are congruent, angles \u22201 and \u22205 are <strong>congruent<\/strong>, and \u22202 and \u22204 are <strong>congruent<\/strong>.<\/p>\n\n\n\n<p>So:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u22201 = \u22205 = 29\u00b0<\/strong><\/li>\n\n\n\n<li><strong>\u22202 = \u22204 = 61\u00b0<\/strong><\/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\">Final Answers:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>m\u22201 = 29\u00b0<\/strong><\/li>\n\n\n\n<li><strong>m\u22202 = 61\u00b0<\/strong><\/li>\n\n\n\n<li><strong>m\u22203 = 90\u00b0<\/strong><\/li>\n\n\n\n<li><strong>m\u22204 = 61\u00b0<\/strong><\/li>\n\n\n\n<li><strong>m\u22205 = 29\u00b0<\/strong><\/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\">Explanation<\/h3>\n\n\n\n<p>In geometry, understanding the properties of rectangles is essential to solve problems involving angle measures. A rectangle is a quadrilateral with four right angles (each 90\u00b0). One critical property is that its diagonals are equal in length and divide the rectangle into two congruent right triangles. This means each triangle will have a 90\u00b0 angle at the corner of the rectangle, and the remaining two angles will sum to 90\u00b0, because the total of any triangle\u2019s angles is 180\u00b0.<\/p>\n\n\n\n<p>In this specific problem, we&#8217;re given that angle \u22204 is 61\u00b0. Since it&#8217;s in a triangle formed by drawing a diagonal in the rectangle, and one angle in a rectangle\u2019s corner is always 90\u00b0, we can use the triangle angle sum theorem. Subtracting the given angle and the right angle from 180\u00b0 gives us the third angle: 180\u00b0 &#8211; 90\u00b0 &#8211; 61\u00b0 = 29\u00b0. This angle is \u22205.<\/p>\n\n\n\n<p>Due to the symmetry and congruency of the triangles created by the diagonal, angle \u22201 must be equal to angle \u22205 (29\u00b0), and angle \u22202 must be equal to angle \u22204 (61\u00b0). The corner angle \u22203 is a right angle and measures 90\u00b0, as all rectangle corners do.<\/p>\n\n\n\n<p>Thus, applying basic angle properties, triangle rules, and congruency principles, we determined all unknown angle measures within the rectangle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/05\/learnexams-banner5-103.jpeg\" alt=\"\" class=\"wp-image-220998\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Find the measures of the numbered angles in each rectangle. 7. 21 61\u00b0 4. 3. 5. Find the measures of the numbered angles in each rectangle. Angle 1 Angle 2 Angle 3 Angle 4 Angle 5\u00a0\u00a01. A rectangle is a parallelogram. sometimes A rhombus is a square. 2. 3. A parallelogram is a rhombus. never [&hellip;]<\/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-220997","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/220997","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=220997"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/220997\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=220997"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=220997"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=220997"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}