NCERT Solutions for Class 8 Maths<\/a> Chapter 3 Understanding Quadrilaterals Ex 3.2 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\nNCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Exercise 3.2<\/h2>\n Question 1. \nFind x in the following figures. \n \nSolution: \n(a) Sum of all the exterior angles of a polygon = 360\u00b0 \n\u21d2 125\u00b0 + 125\u00b0 + x\u00b0 = 360\u00b0 \n\u21d2 250\u00b0 + x = 360\u00b0 \n\u21d2 x = 360\u00b0 – 250\u00b0 \n\u21d2 x = 110\u00b0<\/p>\n
(b) x + 90\u00b0 + 60\u00b0 + 90\u00b0 + 70\u00b0 = 360\u00b0 \n\u21d2 x + 310\u00b0 = 360\u00b0 \n\u21d2 x = 360\u00b0 – 310\u00b0 \n\u21d2 x = 50\u00b0<\/p>\n
Question 2. \nFind the measure of each exterior angle of a regular polygon of \n(i) 9 sides \n(ii) 15 sides \nSolution: \n(i) Number of sides (n) = 9 \nNumber of exterior angles = 9 \nThe given polygon is a regular polygon \nAll the exterior angles are equal \nMeasure of an exterior angle = \\(\\frac{360^{\\circ}}{9}\\) = 40\u00b0<\/p>\n
(ii) Number of sides of regular polygon = 15 \nNumber of equal exterior angles =15 \nThe sum of all the exterior angles = 360\u00b0 \nThe measure of each exterior angle = \\(\\frac{360^{\\circ}}{15}\\) = 24\u00b0<\/p>\n
Question 3. \nHow many sides does a regular polygon have if the measure of an exterior angle is 24\u00b0? \nSolution: \nFor a regular polygon, measure of each angle is equal \nSum of all the exterior angles = 360\u00b0 \nMeasure of an exterior angle = 24\u00b0 \nNumber of sides = \\(\\frac{360^{\\circ}}{24^{\\circ}}\\) = 15 \nThus, there are 15 sides of the regular polygon.<\/p>\n
Question 4. \nHow many sides does a regular polygon have if each of its interior angles is 165\u00b0? \nSolution: \nThe given polygon is a regular polygon. \nEach interior angle = 165\u00b0 \nEach exterior angle =180\u00b0 – 165\u00b0 = 15\u00b0 \nNumber of sides = \\(\\frac{360^{\\circ}}{15^{\\circ}}\\) = 24 \nThus, there are 24 sides of the polygon.<\/p>\n
Question 5. \n(a) Is it possible to have a regular polygon with measure of each exterior angle 22\u00b0? \n(b) Can it be an interior angle of a regular polygon? Why? \nSolution: \n(a) Each exterior angle = 22\u00b0 \n\u2234 Number of sides = \\(\\frac{360^{\\circ}}{22^{\\circ}}=\\frac{180^{\\circ}}{11^{\\circ}}\\) \nIf it is a regular polygon, then its number of sides must be a whole number. \nHere \\(\\frac{180^{\\circ}}{11^{\\circ}}\\) is not a whole number. \n\u2234 22\u00b0 cannot be an exterior angle of a regular polygon.<\/p>\n
(b) If 22\u00b0 is an interior angle, then \n(180\u00b0 – 22\u00b0) = 158\u00b0 is an exterior angle. \n\u2234 Number of sides = \\(\\frac{360^{\\circ}}{158^{\\circ}}=\\frac{180^{\\circ}}{79^{\\circ}}\\) \n\\(\\frac{180^{\\circ}}{79^{\\circ}}\\) is not a whole number \n\u2234 22\u00b0 cannot be an interior angle of a regular polygon.<\/p>\n
Question 6. \n(a) What is the minimum interior angle possible for a regular polygon? Why? \n(b) What is the maximum exterior angle possible for a regular polygon? \nSolution: \n(a) The minimum number of sides of a polygon = 3 \nThe regular polygon of 3 sides is an equilateral triangle. \n\u2234 Each interior angle of an equilateral triangle is 60\u00b0.<\/p>\n
(b) The sum of an exterior angle and its corresponding interior angle is 180\u00b0. \nMinimum interior angle of a regular polygon is 60\u00b0. \n\u2234 The maximum exterior angle of a regular polygon = 180\u00b0 – 60\u00b0 = 120\u00b0<\/p>\n","protected":false},"excerpt":{"rendered":"
These NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Exercise 3.2 Question 1. Find x in the following figures. Solution: (a) Sum of all the exterior angles of a polygon …<\/p>\n
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","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":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":""},"categories":[7],"tags":[],"yoast_head":"\nNCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 - MCQ Questions<\/title>\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\t \n\t \n\t \n