# NCERT Solutions for Class 8 Maths Chapter 3- Understanding Quadrilaterals Exercise 3.1

The NCERT solutions for Class 8 maths Chapter 3- Understanding Quadrilaterals contains solutions for all exercise questions. The subject experts at BYJUâ€™S have solved each question of NCERT exercises meticulously to help the students in solving any question from the NCERT textbook. NCERT Class 8 Exercise 3.1 is based on polygons and classification of polygons. Students can download the NCERT Solutions of Class 8 Mathematics to sharpen their skills.

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### Access other exercise solutions of Class 8 Maths Chapter 3- Understanding Quadrilaterals

Exercise 3.2 Solutions 6 Questions (6 Short Answer Questions)

Exercise 3.3 Solutions 12 Questions (6 Long Answer Questions, 6 Short Answer Questions)

Exercise 3.4 Solutions 6 Questions (1 Long Answer Questions, 5 Short Answer Questions)

### Access Answers to NCERT Class 8 Maths Chapter 3- Understanding Quadrilaterals Exercise 3.1 Page Number 41

1. Given here are some figures.

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Classify each of them on the basis of the following.

Simple curve (b) Simple closed curve (c) Polygon

(d) Convex polygon (e) Concave polygon

Solution:

a) Simple curve: 1, 2, 5, 6 and 7

b) Simple closed curve: 1, 2, 5, 6 and 7

c) Polygon: 1 and 2

d) Convex polygon: 2

e) Concave polygon: 1

2. How many diagonals does each of the following have?

a) A convex quadrilateral (b) A regular hexagon (c) A triangle

Solution:

b) A regular hexagon: 9.

c) A triangle: 0

3. 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!)

Solution:

Let ABCD be a convex quadrilateral.

From the figure, we infer that the quadrilateral ABCD is formed by two triangles,

Since, we know that sum of interior angles of triangle is 180Â°,

the sum of the measures of the angles is 180Â° + 180Â° = 360Â°

Let us take another quadrilateral ABCD which is not convex .

Join BC, Such that it divides ABCD into two triangles Î”ABC and Î”BCD. In Î”ABC,

âˆ 1 + âˆ 2 + âˆ 3 = 180Â° (angle sum property of triangle)

In Î”BCD,

âˆ 4 + âˆ 5 + âˆ 6 = 180Â° (angle sum property of triangle)

âˆ´, âˆ 1 + âˆ 2 + âˆ 3 + âˆ 4 + âˆ 5 + âˆ 6 = 180Â° + 180Â°

â‡’ âˆ 1 + âˆ 2 + âˆ 3 + âˆ 4 + âˆ 5 + âˆ 6 = 360Â°

â‡’ âˆ A + âˆ B + âˆ C + âˆ D = 360Â°

Thus, this property hold if the quadrilateral is not convex.

4. Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)

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What can you say about the angle sum of a convex polygon with number of sides? (a) 7 (b) 8 (c) 10 (d) n

Solution:

The angle sum of a polygon having side n = (n-2)Ã—180Â°

a) 7

Here, n = 7

Thus, angle sum = (7-2)Ã—180Â° = 5Ã—180Â° = 900Â°

b) 8

Here, n = 8

Thus, angle sum = (8-2)Ã—180Â° = 6Ã—180Â° = 1080Â°

c) 10

Here, n = 10

Thus, angle sum = (10-2)Ã—180Â° = 8Ã—180Â° = 1440Â°

d) n

Here, n = n

Thus, angle sum = (n-2)Ã—180Â°

5. What is a regular polygon?

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State the name of a regular polygon of

(i) 3 sides (ii) 4 sides (iii) 6 sides Solution:

Regular polygon: A polygon having sides of equal length and angles of equal measures is called regular polygon. i.e., A regular polygon is both equilateral and equiangular.

(i) A regular polygon of 3 sides is called equilateral triangle.

(ii) A regular polygon of 4 sides is called square.

(iii) A regular polygon of 6 sides is called regular hexagon.

6. Find the angle measure x in the following figures.

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Solution:

a) The figure is having 4 sides. Hence, it is a quadrilateral. Sum of angles of the quadrilateral = 360Â°

â‡’ 50Â° + 130Â° + 120Â° + x = 360Â°

â‡’ 300Â° + x = 360Â°

â‡’ x = 360Â° â€“ 300Â° = 60Â°

b) The figure is having 4 sides. Hence, it is a quadrilateral. Also, one side is perpendicular forming right angle.

Sum of angles of the quadrilateral = 360Â°

â‡’ 90Â° + 70Â° + 60Â° + x = 360Â°

â‡’ 220Â° + x = 360Â°

â‡’ x = 360Â° â€“ 220Â° = 140Â°

c) The figure is having 5 sides. Hence, it is a pentagon.

Sum of angles of the pentagon = 540Â° Two angles at the bottom are linear pair.

âˆ´, 180Â° â€“ 70Â° = 110Â°

180Â° â€“ 60Â° = 120Â°

â‡’ 30Â° + 110Â° + 120Â° + x + x = 540Â°

â‡’ 260Â° + 2x = 540Â°

â‡’ 2x = 540Â° â€“ 260Â° = 280Â°

â‡’ 2x = 280Â°

= 140Â°

d) The figure is having 5 equal sides. Hence, it is a regular pentagon. Thus, its all angles are equal.

5x = 540Â°

â‡’ x = 540Â°/5

â‡’ x = 108Â°

7.

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Solution:

a) Sum of all angles of triangle = 180Â°

One side of triangle = 180Â°- (90Â° + 30Â°) = 60Â°

x + 90Â° = 180Â° â‡’ x = 180Â° â€“ 90Â° = 90Â°

y + 60Â° = 180Â° â‡’ y = 180Â° â€“ 60Â° = 120Â°

z + 30Â° = 180Â° â‡’ z = 180Â° â€“ 30Â° = 150Â°

x + y + z = 90Â° + 120Â° + 150Â° = 360Â°

b) Sum of all angles of quadrilateral = 360Â°

One side of quadrilateral = 360Â°- (60Â° + 80Â° + 120Â°) = 360Â° â€“ 260Â° = 100Â°

x + 120Â° = 180Â° â‡’ x = 180Â° â€“ 120Â° = 60Â°

y + 80Â° = 180Â° â‡’ y = 180Â° â€“ 80Â° = 100Â°

z + 60Â° = 180Â° â‡’ z = 180Â° â€“ 60Â° = 120Â°

w + 100Â° = 180Â° â‡’ w = 180Â° â€“ 100Â° = 80Â°

x + y + z + w = 60Â° + 100Â° + 120Â° + 80Â° = 360Â°

Exercise 3.1 of NCERT Solutions for Class 8 Maths Chapter 3- Understanding Quadrilaterals is based on the following topics:

1. Introduction
2. Polygons
1. Classification of Polygons
2. Diagonals
3. Convex and Concave Polygons
4. Regular and Irregular Polygons
5. Angle sum property