{"id":26912,"date":"2021-06-28T16:56:54","date_gmt":"2021-06-28T11:26:54","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=26912"},"modified":"2022-03-02T10:47:27","modified_gmt":"2022-03-02T05:17:27","slug":"ncert-solutions-for-class-8-maths-chapter-3-ex-3-1","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-8-maths-chapter-3-ex-3-1\/","title":{"rendered":"NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.1"},"content":{"rendered":"

These NCERT Solutions for Class 8 Maths<\/a> Chapter 3 Understanding Quadrilaterals Ex 3.1 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\n

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Exercise 3.1<\/h2>\n

Question 1.
\nGiven here are some figures.
\n\"NCERT
\nClassify each of them on the basis of the following.
\n(a) Simple curve
\n(b) Simple closed curve
\n(c) Polygon
\n(d) Convex polygon
\n(e) Concave polygon
\nSolution:
\n(a) Simple curves are: (1), (2), (5) (6) and (7)
\n(b) Simple closed curves are: (1), (2), (5), (6) and (7) and (4)
\n(c) Polygons are: (1) and (2)
\n(d) Convex polygon is (2)
\n(e) Concave polygon is (1) and (4)<\/p>\n

\"NCERT<\/p>\n

Question 2.
\nHow many diagonals does each of the following have?
\n(a) A convex quadrilateral
\n(b) A regular hexagon
\n(c) A triangle
\nSolution:
\nNote: Number of diagonals in a polygon having n sides
\nn-side = \\(\\left[\\frac{n(n-1)}{2}-n\\right]\\)
\n(a) In quadrilateral, number of sides (n) = 4
\nNumber of diagonals = 2
\n\\(\\left[\\frac{4(4-1)}{2}-4=\\frac{4 \\times 3}{2}-4=6-4=2\\right]\\)<\/p>\n

(b) In a regular hexagon number of sides, (n) = 6
\n\\(\\left[\\frac{6(6-1)}{2}-6=\\frac{6 \\times 5}{2}-6=15-6=9\\right]\\)<\/p>\n

(c) In a triangle, number of sides (n) = 3
\n\u2234 Number of diagonals = \\(\\frac{n(n-1)}{2}-n\\)
\n= \\(\\frac{3(3-1)}{2}\\) – 3
\n= \\(\\frac{3 \\times 2}{2}\\) – 3
\n= 3 – 3
\n= 0<\/p>\n

Question 3.
\nWhat is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)
\nSolution:
\nThe sum of the measures of the angles of a convex quadrilateral is 360\u00b0
\nYes, this property holds, even if the quad-rilateral is not convex.<\/p>\n

\"NCERT<\/p>\n

Question 4.
\nExamine the table.
\nEach (figure is divided into triangles and the sum of the angles deduced from that).
\n\"NCERT
\nWhat can you say about the angle sum of a convex polygon with number of sides?
\n(a) 7
\n(b) 8
\n(c) 10
\n(d) n
\nSolution:
\n(a) When n = 7
\nSum of interior angles of a polygon = (7 – 2) \u00d7 180\u00b0
\n= 5 \u00d7 180\u00b0
\n= 900\u00b0<\/p>\n

(b) When n = 8
\nSum of interior angles of a polygon = (8 – 2) \u00d7 180\u00b0
\n= 6 \u00d7 180\u00b0
\n= 1080\u00b0<\/p>\n

(c) When n = 10
\nSum of interior angles of a polygon having 10 sides = (10 – 2) \u00d7 180\u00b0
\n= 8 \u00d7 180\u00b0
\n= 1440\u00b0<\/p>\n

(d) When n = n
\nSum of interior angles of a polygon = (n – 2) \u00d7 180\u00b0<\/p>\n

Question 5.
\nWhat is a regular polygon?
\nState the name of a regular polygon of
\n(i) 3 sides
\n(ii) 4 sides
\n(iii) 6 sides
\nSolution:
\nA polygon is said to be a regular polygon if
\n(a) The measures of its interior angles are equal
\n(b) The length of its sides are equal
\nThe name of a regular polygon having
\n(i) 3 sides is \u2018equilateral triangle\u2019
\n(ii) 4 sides is \u2018square\u2019.
\n(iii) 6 sides is \u2018regular hexagon’.<\/p>\n

\"NCERT<\/p>\n

Question 6.
\nFind the angle measure x in the following figures.
\n\"NCERT
\nSolution:
\n(a) The sum of interior angles of a quadrilateral is 360\u00b0
\n\u2234 x + 120\u00b0 + 130\u00b0 + 50\u00b0 = 360\u00b0
\n\u21d2 x + 300\u00b0 = 360\u00b0
\n\u21d2 x = 360\u00b0 – 300\u00b0
\n\u21d2 x = 60\u00b0<\/p>\n

(b) The sum of the interior angles of a quadrilateral is 360\u00b0
\n\u2234 x + 70\u00b0 + 60\u00b0 + 90\u00b0 = 360\u00b0
\n\u21d2 x + 220\u00b0 = 360\u00b0
\n\u21d2 x = 360\u00b0 – 220\u00b0
\n\u21d2 x = 140\u00b0<\/p>\n

(c) Interior angles are 30\u00b0, x\u00b0, (180 – 60\u00b0), (180\u00b0 – 70\u00b0) and x\u00b0
\ni.e., 30\u00b0, x\u00b0, 120\u00b0, 110\u00b0 and x\u00b0
\nThe given figure is a pentagon.
\nSum of interior angles of a pentagon = 540\u00b0
\n\u2234 30\u00b0 + x \u00b0 + 120\u00b0 + 110\u00b0 + x = 540\u00b0
\n\u21d2 2x\u00b0 + 260\u00b0 = 540\u00b0
\n\u21d2 2x\u00b0 = 540\u00b0 – 260\u00b0
\n\u21d2 2x\u00b0= 280\u00b0
\n\u21d2 x = \\(\\frac{280^{\\circ}}{2}\\)
\n\u21d2 x = 140\u00b0
\nThe measure of x is 140\u00b0.<\/p>\n

(d) It is a regular pentagon.
\nSum of all the interior angles of regular pentagon = 540\u00b0
\nIt’s each angle is equal to x\u00b0.
\nx\u00b0 + x\u00b0 + x\u00b0 + x\u00b0 + x\u00b0 = 540\u00b0
\n\u21d2 5x\u00b0 = 540\u00b0
\n\u21d2 x = \\(\\frac{540^{\\circ}}{5}\\)
\n\u21d2 x = 108\u00b0
\nThe measure of x is 108\u00b0.<\/p>\n

\"NCERT<\/p>\n

Question 7.
\n\"NCERT
\n(a) Find x + y + z
\n\"NCERT
\n(b) Find x + y + z + w
\nSolution:
\n(a) x + 90\u00b0 = 180\u00b0 (Linear Pair)
\nx = 180\u00b0 – 90\u00b0 = 90\u00b0
\ny = 30\u00b0 + 90\u00b0 [\u2235 exterior angle of a triangle is equal to the sum of interior opposite angles]
\n\u21d2 y = 120\u00b0
\nz + 30\u00b0 = 180\u00b0 (Linear pair)
\n\u21d2 z = 180\u00b0 – 30\u00b0 = 150\u00b0
\n\u2234 x + y + z = 90\u00b0 + 120\u00b0 + 150\u00b0 = 360\u00b0<\/p>\n

(b) The sum of interior angles of a quadrilateral = 360\u00b0
\n\u21d2 \u22201 + 120\u00b0 + 80\u00b0 + 60\u00b0 = 360\u00b0
\n\u21d2 \u22201 + 260\u00b0 = 360\u00b0
\n\u21d2 \u22201 = 360\u00b0 – 260\u00b0 = 100\u00b0
\nNow, x + 120\u00b0 = 180\u00b0 (linear pair)
\nx = 180\u00b0 – 120\u00b0 = 60\u00b0
\ny + 80\u00b0 = 180\u00b0 (Linear pair)
\n\u21d2 y = 180\u00b0 – 80\u00b0 = 100\u00b0
\nz + 60\u00b0 = 180\u00b0 (Linear pair)
\n\u21d2 z = 180\u00b0 – 60\u00b0
\n\u21d2 z = 120\u00b0
\nw + \u22201 = 180\u00b0 (Linear Pair)
\n\u21d2 w + 100\u00b0= 180\u00b0
\n\u21d2 w = 180\u00b0 – 100\u00b0 = 80\u00b0
\nThus x + y + z + w = 60\u00b0 + 100\u00b0 + 120\u00b0 + 80\u00b0 = 360\u00b0<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.1 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Exercise 3.1 Question 1. Given here are some figures. Classify each of them on the basis of the following. (a) Simple …<\/p>\n

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.1<\/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 3.1 - MCQ Questions<\/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:\/\/mcq-questions.com\/ncert-solutions-for-class-8-maths-chapter-3-ex-3-1\/\" \/>\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 3.1 - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.1 Questions and Answers are prepared by our highly skilled subject experts. 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