{"id":26933,"date":"2021-06-28T17:39:24","date_gmt":"2021-06-28T12:09:24","guid":{"rendered":"https:\/\/ncertsolutions.guru\/?p=26933"},"modified":"2021-06-28T17:39:24","modified_gmt":"2021-06-28T12:09:24","slug":"ncert-solutions-for-class-8-maths-chapter-3-ex-3-2","status":"publish","type":"post","link":"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-8-maths-chapter-3-ex-3-2\/","title":{"rendered":"NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2"},"content":{"rendered":"

These 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>\n

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Exercise 3.2<\/h2>\n

Question 1.
\nFind x in the following figures.
\n\"NCERT
\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":{"spay_email":""},"categories":[7],"tags":[],"yoast_head":"\nNCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 - NCERT Solutions<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-8-maths-chapter-3-ex-3-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 - NCERT Solutions\" \/>\n<meta property=\"og:description\" content=\"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. 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