NCERT Solutions Class 8 Maths Chapter 3 Understanding Quadrilaterals – Here are all the NCERT solutions for Class 8 Maths Chapter 3. This solution contains questions, answers, images, explanations of the complete chapter 3 titled Understanding Quadrilaterals of Maths taught in class 8. If you are a student of class 8 who is using NCERT Textbook to study Maths, then you must come across chapter 3 Understanding Quadrilaterals. After you have studied lesson, you must be looking for answers of its questions. Here you can get complete NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals in one place.
NCERT Solutions Class 8 Maths Chapter 3 Understanding Quadrilaterals
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For a better understanding of this chapter, you should also see summary of Chapter 3 Understanding Quadrilaterals , Maths, Class 8.
| Class | 8 |
| Subject | Maths |
| Book | Mathematics |
| Chapter Number | 3 |
| Chapter Name |
Understanding Quadrilaterals |
NCERT Solutions Class 8 Maths chapter 3 Understanding Quadrilaterals
Class 8, Maths chapter 3, Understanding Quadrilaterals solutions are given below in PDF format. You can view them online or download PDF file for future use.
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Question & Answer
Q.1: Given here are some figures.
Classify each of them on the basis of the following.
(a) Simple curve (b) Simple closed curve (c) Polygon (d) Convex polygon (e) Concave polygon.
Ans : (a) 1, 2, 5, 6, 7 (b) 1, 2, 5, 6, 7 (c) 1, 2 (d) 2 (e) 1
Q.2: What 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!)
Ans : The sum of the measures of the angles of a convex quadrilateral is 3600 as a convex quadrilateral is made of two triangles.Here, ABCD is a convex quadrilateral, made Of two triangles \(\triangle A B D\) and \(\triangle B C D\).Therefore, the sum of all the interior angles of this quadrilateral will be same as the sum of all the interior angles of these two triangles i.e., \(180^{\circ}+180^{\circ}=360^{\circ}\) Yes, this property also holds true for a quadrilateral which is not convex. This is because any quadrilateral can be divided into two triangles.
Here again, ABCD is a concave quadrilateral, made of two triangles \(\triangle A B D\) and \(\triangle B C D\) . Therefore, sum of all the interior angles of this quadrilateral will also be \(180^{\circ}+180^{\circ}=360^{\circ}\).
Q.3: Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)
What can you say about the angle sum of a convex polygon with number of sides? (a) 7
(b) 8
(c) 10
(d) n
Ans : From the table, it can be observed that the angle sum of a convex polygon of n sides is (n —2) x \(180^{\circ}\). Hence, the angle sum of the convex polygons having number of sides as above will be as follows. (a) (7 - 2) x \(180^{\circ}\) = \(900^{\circ}\) (b) (8 - 2) x \(180^{\circ}\) = \(1800^{\circ}\) (c) (10 - 2) x \(180^{\circ}\) = \(180^{\circ}\) (d) (n - 2) x \(180^{\circ}\)
Q.4: What is a regular polygon?
State the name of a regular polygon of
(i) 3 sides
(ii) 4 sides
(iii) 6 sides
Ans : A polygon with equal sides and equal angles is called a regular polygon.
Q.5: Find the angle measure x in the following figures.
Ans : (a) Sum of the measures of all interior angles of a quadrilateral is \(360^{\circ}\) Therefore, in the given quadrilateral, \(50^{\circ}\) + \(130^{\circ}\) + \(120^{\circ}\) + x = \(360^{\circ}\) \(300^{\circ}\) + x = \(360^{\circ}\) x = \(60^{\circ}\) (b)From the figure, it can be concluded that, \(90^{\circ}\) + a = \(180^{\circ}\) (Linear pair) a = \(180^{\circ}\) - \(90^{\circ}\) = \(90^{\circ}\) Sum Of the measures Of all interior angles of a quadrilateral is \(360^{\circ}\). Therefore, in the given quadrilateral, \(60^{\circ}\) + \(70^{\circ}\) + x + \(90^{\circ}\) = \(360^{\circ}\) \(220^{\circ}\) + x = \(360^{\circ}\) x = \(140^{\circ}\) (c)
From the figure, it can be concluded that, 70 + a = \(180^{\circ}\) (Linear pair) a = \(110^{\circ}\) \(60^{\circ}\) + b = \(180^{\circ}\) (Linear pair) b = \(120^{\circ}\) Sum Of the measures Of all interior angles Of a pentagon is \(540^{\circ}\), Therefore, in the given pentagon, \(120^{\circ}\) + \(110^{\circ}\) + \(30^{\circ}\) + x + x = \(540^{\circ}\) \(260^{\circ}\) + 2x = \(540^{\circ}\) 2x = \(280^{\circ}\) X = \(140^{\circ}\) (d) Sum of the measures of all interior angles of a pentagon is \(540^{\circ}\) 5x = \(540^{\circ}\) x = \(108^{\circ}\)
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