{"id":3024,"date":"2022-12-02T12:00:35","date_gmt":"2022-12-02T12:00:35","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=3024"},"modified":"2023-01-31T06:55:59","modified_gmt":"2023-01-31T06:55:59","slug":"ncert-solutions-class-8-maths-chapter-3-understanding-quadrilaterals-ex-3-2","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-3-understanding-quadrilaterals-ex-3-2\/","title":{"rendered":"NCERT Solutions Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 8 Mathematics\u00a0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 3 (Understanding Quadrilaterals)\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 8 Mathematics <strong>Chapter &#8211; 3 Understanding Quadrilaterals <\/strong>Exercise 3.2 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<h4><span style=\"color: #000000;\"><strong>Chapter 3: Understanding Quadrilaterals<\/strong><\/span><\/h4>\n<ul>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-3-understanding-quadrilaterals-ex-3-1\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 3.1<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-3-understanding-quadrilaterals-ex-3-3\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 3.3<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-3-understanding-quadrilaterals-ex-3-4\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 3.4<\/a><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 3.2\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>1. Find x in the following figures.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3045\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/11\/NCERT-Solutions-Class-8-Maths-Ex-3.2-Q-1.png\" alt=\"NCERT Maths Solutions Class 8\" width=\"720\" height=\"253\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/11\/NCERT-Solutions-Class-8-Maths-Ex-3.2-Q-1.png 720w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/11\/NCERT-Solutions-Class-8-Maths-Ex-3.2-Q-1-300x105.png 300w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/11\/NCERT-Solutions-Class-8-Maths-Ex-3.2-Q-1-480x169.png 480w\" sizes=\"auto, (max-width: 720px) 100vw, 720px\" \/><br \/>\n<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(a)<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3046\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/11\/NCERT-Solutions-Class-8-Maths-Ex-3.2-Q-1a.png\" alt=\"NCERT Maths Solutions Class 8\" width=\"245\" height=\"200\" \/><br \/>\n<\/strong>125\u00b0 + m = 180\u00b0 \u21d2 m = 180\u00b0 \u2013 125\u00b0 = 55\u00b0 (Linear pair)<br \/>\n125\u00b0 + n = 180\u00b0 \u21d2 n = 180\u00b0 \u2013 125\u00b0 = 55\u00b0 (Linear pair)<br \/>\nx = m + n (The exterior angle of a triangle is equal to the sum of the two opposite interior angles)<br \/>\n\u21d2 x = 55\u00b0 + 55\u00b0 = 110\u00b0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(b)<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3047\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/11\/NCERT-Solutions-Class-8-Maths-Ex-3.2-Q-1b.png\" alt=\"NCERT Maths Solutions Class 8\" width=\"279\" height=\"253\" \/><br \/>\n<\/strong>Two interior angles are right angles = 90\u00b0<br \/>\n70\u00b0 + m = 180\u00b0 \u21d2 m = 180\u00b0 \u2013 70\u00b0 = 110\u00b0 (Linear pair)<br \/>\n60\u00b0 + n = 180\u00b0 \u21d2 n = 180\u00b0 \u2013 60\u00b0 = 120\u00b0 (Linear pair) The figure is having five sides and is a pentagon.<br \/>\nThus, sum of the angles of a pentagon = 540\u00b0<br \/>\n\u21d2 90\u00b0 + 90\u00b0 + 110\u00b0 + 120\u00b0 + y = 540\u00b0<br \/>\n\u21d2 410\u00b0 + y = 540\u00b0 \u21d2 y = 540\u00b0 \u2013 410\u00b0 = 130\u00b0<br \/>\nx + y = 180\u00b0 (Linear pair)<br \/>\n\u21d2 x + 130\u00b0 = 180\u00b0<br \/>\n\u21d2 x = 180\u00b0 \u2013 130\u00b0 = 50\u00b0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>2. Find the measure of each exterior angle of a regular polygon of<br \/>\n<\/strong><strong>(i) 9 sides<br \/>\n(ii) 15 sides<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong><strong>(i)<\/strong> Each exterior angle = Sum of exterior angles\/Number of angles = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{360}{9}\" alt=\"\\frac{360}{9}\" align=\"absmiddle\" \/> = 40\u00b0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) <\/strong>Each exterior angle = sum of exterior angles\/Number of angles = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{360}{15}\" alt=\"\\frac{360}{15}\" align=\"absmiddle\" \/> = 24\u00b0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>3. How many sides does a regular polygon have if the measure of an exterior angle is 24\u00b0?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211; <\/strong>Each exterior angle = sum of exterior angles\/Number of angles<br \/>\n24\u00b0 = 360\/ Number of sides<br \/>\n\u21d2 Number of sides = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{360}{24}\" alt=\"\\frac{360}{24}\" align=\"absmiddle\" \/> = 15<br \/>\nThus, the regular polygon has 15 sides.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>4. How many sides does a regular polygon have if each of its interior angles is 165\u00b0?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>Interior angle = 165\u00b0<br \/>\nExterior angle = 180\u00b0 \u2013 165\u00b0 = 15\u00b0<br \/>\nNumber of sides = sum of exterior angles\/exterior angles<br \/>\n\u21d2 Number of sides = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{360}{15}\" alt=\"\\frac{360}{15}\" align=\"absmiddle\" \/> = 24\u00b0<br \/>\nThus, the regular polygon has 24 sides.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>5.<br \/>\n<\/strong><strong>(a) Is it possible to have a regular polygon with measure of each exterior angle as 22\u00b0?<br \/>\n<\/strong><strong>(b) Can it be an interior angle of a regular polygon? Why?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(a)<\/strong> Exterior angle = 22\u00b0<br \/>\nNumber of sides = sum of exterior angles\/ exterior angle<br \/>\n\u21d2 Number of sides = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{360}{22}\" alt=\"\\frac{360}{22}\" align=\"absmiddle\" \/> = 16.36<br \/>\nNo, we can\u2019t have a regular polygon with each exterior angle as 22\u00b0 as it is not a divisor of 360.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(b)<\/strong> Interior angle = 22\u00b0<br \/>\nExterior angle = 180\u00b0 \u2013 22\u00b0= 158\u00b0<br \/>\nNo, we can\u2019t have a regular polygon with each exterior angle as 158\u00b0 as it is not a divisor of 360.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>6.\u00a0<\/strong><strong><br \/>\n(a) What is the minimum interior angle possible for a regular polygon? Why?<br \/>\n<\/strong><strong>(b) What is the maximum exterior angle possible for a regular polygon?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(a)<\/strong> An equilateral triangle is the regular polygon (with 3 sides) having the least possible minimum interior angle because a regular polygon can be constructed with minimum 3 sides.<br \/>\nSince the sum of interior angles of a triangle = 180\u00b0<br \/>\nEach interior angle = 180\/3 = 60\u00b0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(b)<\/strong> An equilateral triangle is the regular polygon (with 3 sides) having the maximum exterior angle because the regular polygon with the least number of sides has the maximum exterior angle possible. Maximum exterior possible = 180 \u2013 60\u00b0 = 120\u00b0<\/span><\/p>\n<p>&nbsp;<\/p>\n<table style=\"width: 100%; border-collapse: collapse;\" border=\"1\">\n<tbody>\n<tr style=\"height: 32px;\">\n<td style=\"width: 100%; background-color: #f2e079; text-align: center; height: 32px;\"><span style=\"color: #ff0000; font-size: 14pt;\"><strong>NCERT Class 8<sup>th\u00a0<\/sup>Solution\u00a0<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-english\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 English\u201d (Edit)\">NCERT Solutions Class 8 English<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-hindi\/\" aria-label=\"\u201cNCERT Solutions Class 6 Maths\u201d (Edit)\">NCERT Solutions Class 8 Hindi<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Maths\u201d (Edit)\">NCERT Solutions Class 8 Mathematics<\/a>\u00a0<\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-sanskrit-ruchira\/\" target=\"_blank\" rel=\"noopener\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\">NCERT Solutions Class 8 Sanskrit<\/span><\/strong><\/span><\/a><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-science\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Social Science\u201d (Edit)\">NCERT Solutions Class 8 Science<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-social-science\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Social Science\u201d (Edit)\">NCERT Solutions Class 8 Social Science<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 8 Mathematics\u00a0 Chapter &#8211; 3 (Understanding Quadrilaterals)\u00a0 The NCERT Solutions in English Language for Class 8 Mathematics Chapter &#8211; 3 Understanding Quadrilaterals Exercise 3.2 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter 3: Understanding Quadrilaterals NCERT Solution Class 8 Maths Ex &#8211; 3.1 NCERT [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[442],"tags":[448,449,445,5],"class_list":["post-3024","post","type-post","status-publish","format-standard","hentry","category-class-8-maths","tag-ncert-class-8-maths-chapter-3-understanding-quadrilaterals-in-english","tag-ncert-solutions-class-8-maths-chapter-3-in-english","tag-ncert-solutions-class-8-maths-in-english","tag-ncert-solutions-in-english"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.3) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>NCERT Solutions Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 | TheExamPillar NCERT<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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