{"id":108315,"date":"2022-02-12T15:41:06","date_gmt":"2022-02-12T10:11:06","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=108315"},"modified":"2025-06-20T13:12:18","modified_gmt":"2025-06-20T07:42:18","slug":"ncert-solutions-for-class-8-maths-chapter-3-understanding-quadrilaterals-ex-3-2","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/ncert-solutions\/class-8\/maths\/ncert-solutions-for-class-8-maths-chapter-3-understanding-quadrilaterals-ex-3-2\/","title":{"rendered":"NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2"},"content":{"rendered":"<h2>NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2<\/h2>\n<p><strong>NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Exercise 3.2<\/strong><\/p>\n<p>Ex 3.2 Class 8 Maths Question 1.<br \/>\nFind x in the following figures.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-105995\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Solutions-for-Class-8-Maths-Chapter-3-Understanding-Quadrilaterals-Ex-3.2-Q1.png\" alt=\"NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Q1\" width=\"368\" height=\"151\" \/><br \/>\nSolution:<br \/>\n(a) We know that the sum of all the exterior angles of a polygon = 360\u00b0<br \/>\n125\u00b0 + 125\u00b0 + x = 360\u00b0<br \/>\n\u21d2 250\u00b0 + x = 360\u00b0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-105993\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Solutions-for-Class-8-Maths-Chapter-3-Understanding-Quadrilaterals-Ex-3.2-Q1.1.png\" alt=\"NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Q1.1\" width=\"166\" height=\"133\" \/><br \/>\nx = 360\u00b0 \u2013 250\u00b0 = 110\u00b0<br \/>\nHence x = 110\u00b0<br \/>\n(b) Here \u2220y = 180\u00b0 \u2013 90\u00b0 = 90\u00b0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-105994\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Solutions-for-Class-8-Maths-Chapter-3-Understanding-Quadrilaterals-Ex-3.2-Q1.2.png\" alt=\"NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Q1.2\" width=\"173\" height=\"150\" \/><br \/>\nand \u2220z = 90\u00b0 (given)<br \/>\nx + y + 60\u00b0 + z + 70\u00b0 = 360\u00b0 [\u2235 Sum of all the exterior angles of a polygon = 360\u00b0]\n\u21d2 x + 90\u00b0 + 60\u00b0 + 90\u00b0 + 70\u00b0 = 360\u00b0<br \/>\n\u21d2 x + 310\u00b0 = 360\u00b0<br \/>\n\u21d2 x = 360\u00b0 \u2013 310\u00b0 = 50\u00b0<br \/>\nHence x = 50\u00b0<\/p>\n<p>Ex 3.2 Class 8 Maths Question 2.<br \/>\nFind the measure of each exterior angle of a regular polygon of<br \/>\n(i) 9 sides<br \/>\n(ii) 15 sides<br \/>\nSolution:<br \/>\n(i) We know the sum of all the exterior angles of polygon = 360\u00b0<br \/>\nMeasure of each angle of 9 sided regular polygon = \\(\\frac { 360 }{ 9 }\\) = 40\u00b0<br \/>\n(ii) Sum of all the exterior angles of a polygon = 360\u00b0<br \/>\nMeasure of each angle of 15 sided regular polygon = \\(\\frac { 360 }{ 15 }\\) = 24\u00b0<\/p>\n<p>Ex 3.2 Class 8 Maths Question 3.<br \/>\nHow many sides does a regular polygon have if the measure of an exterior angle is 24\u00b0?<br \/>\nSolution:<br \/>\nSum of all exterior angles of a regular polygon = 360\u00b0<br \/>\nNumber of sides<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-105996\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Solutions-for-Class-8-Maths-Chapter-3-Understanding-Quadrilaterals-Ex-3.2-Q3.png\" alt=\"NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Q3\" width=\"189\" height=\"99\" \/><br \/>\nHence, the number of sides = 15<\/p>\n<p>Ex 3.2 Class 8 Maths Question 4.<br \/>\nHow many sides does a regular polygon have if each of its interior angles is 165\u00b0?<br \/>\nSolution:<br \/>\nLet re be the number of sides of a regular polygon.<br \/>\nSum of all interior angles = (n \u2013 2) \u00d7 180\u00b0<br \/>\nand, measure of its each angle<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-105997\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Solutions-for-Class-8-Maths-Chapter-3-Understanding-Quadrilaterals-Ex-3.2-Q4.png\" alt=\"NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Q4\" width=\"276\" height=\"242\" \/><br \/>\nHence, the number of sides = 24<\/p>\n<p>Ex 3.2 Class 8 Maths Question 5.<br \/>\n(a) Is it possible to have a regular polygon with measure of each exterior angle a is 22\u00b0?<br \/>\n(b) Can it be an interior angle of a regular polygon? Why?<br \/>\nSolution:<br \/>\n(a) Since, the sum of all the exterior angles of a regular polygon = 360\u00b0 which is not divisible by 22\u00b0.<br \/>\nIt is not possible that a regular polygon must have its exterior angle 22\u00b0.<br \/>\n(b) Sum of all interior angles of a regular polygon of side n = (n \u2013 2) \u00d7 180\u00b0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-105998\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Solutions-for-Class-8-Maths-Chapter-3-Understanding-Quadrilaterals-Ex-3.2-Q5.png\" alt=\"NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Q5\" width=\"269\" height=\"241\" \/><br \/>\nnot a whole number.<br \/>\nSince number of sides cannot be in fractions.<br \/>\nIt is not possible for a regular polygon to have its interior angle = 22\u00b0.<\/p>\n<p>Ex 3.2 Class 8 Maths Question 6.<br \/>\n(a) What is the minimum interior angle possible for a regular polygon? Why?<br \/>\n(b) What is the maximum exterior angle possible for a regular polygon?<br \/>\nSolution:<br \/>\n(a) Sum of all interior angles of a regular polygon of side n = (n \u2013 2) \u00d7 180\u00b0<br \/>\nThe measure of each interior angle<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-105999\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Solutions-for-Class-8-Maths-Chapter-3-Understanding-Quadrilaterals-Ex-3.2-Q6.png\" alt=\"NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Q6\" width=\"349\" height=\"145\" \/><br \/>\nThe minimum measure the angle of an equilateral triangle (n = 3) = 60\u00b0.<br \/>\n(b) From part (a) we can conclude that the maximum exterior angle of a regular polygon = 180\u00b0 \u2013 60\u00b0 = 120\u00b0.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-105987\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Solutions-for-Class-8-Maths-Chapter-3-Understanding-Quadrilaterals-Ex-3.2-A1.png\" alt=\"NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 A1\" width=\"574\" height=\"279\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-105986\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Solutions-for-Class-8-Maths-Chapter-3-Understanding-Quadrilaterals-Ex-3.2-A1.1.png\" alt=\"NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 A1.1\" width=\"517\" height=\"462\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-105988\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Solutions-for-Class-8-Maths-Chapter-3-Understanding-Quadrilaterals-Ex-3.2-A2.png\" alt=\"NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 A2\" width=\"592\" height=\"447\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-105989\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Solutions-for-Class-8-Maths-Chapter-3-Understanding-Quadrilaterals-Ex-3.2-A3.png\" alt=\"NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 A3\" width=\"656\" height=\"229\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-105990\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Solutions-for-Class-8-Maths-Chapter-3-Understanding-Quadrilaterals-Ex-3.2-A4.png\" alt=\"NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 A4\" width=\"630\" height=\"258\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-105991\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Solutions-for-Class-8-Maths-Chapter-3-Understanding-Quadrilaterals-Ex-3.2-A5.png\" alt=\"NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 A5\" width=\"746\" height=\"362\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-105992\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/02\/NCERT-Solutions-for-Class-8-Maths-Chapter-3-Understanding-Quadrilaterals-Ex-3.2-A6.png\" alt=\"NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 A6\" width=\"759\" height=\"333\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 NCERT Solutions for Class 8 Maths Chapter 3 [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"\"Get NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 on Infinity learn\"","custom_permalink":"ncert-solutions\/class-8\/maths\/ncert-solutions-for-class-8-maths-chapter-3-understanding-quadrilaterals-ex-3-2\/"},"categories":[13,54,19,64,75],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - 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