# NCERT Solutions for Class 8 Maths Chapter 3- Understanding Quadrilaterals Exercise 3.2

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 3.2 is based on the measurement of the exterior angle of a polygon. Students can download the NCERT Solutions of Class 8 mathematics to enhance their problem solving skills.

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

Exercise 3.1 Solutions 7 Questions (1 Long Answer 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 of Maths NCERT Class 8 Chapter 3- Understanding Quadrilaterals Exercise 3.2 Page Number 44

1. Find x in the following figures.

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Solution:

a)

125Â° + m = 180Â° â‡’ m = 180Â° â€“ 125Â° = 55Â° (Linear pair)

125Â° + n = 180Â° â‡’ n = 180Â° â€“ 125Â° = 55Â° (Linear pair)

x = m + n (exterior angle of a triangle is equal to the sum of 2 opposite interior 2 angles)

â‡’ x = 55Â° + 55Â° = 110Â°

b)

Two interior angles are right angles = 90Â°

70Â° + m = 180Â° â‡’ m = 180Â° â€“ 70Â° = 110Â° (Linear pair)

60Â° + n = 180Â° â‡’ n = 180Â° â€“ 60Â° = 120Â° (Linear pair) The figure is having five sides and is a pentagon.

Thus, sum of the angles of pentagon = 540Â° 90Â° + 90Â° + 110Â° + 120Â° + y = 540Â°

â‡’ 410Â° + y = 540Â° â‡’ y = 540Â° â€“ 410Â° = 130Â°

x + y = 180Â° (Linear pair)

â‡’ x + 130Â° = 180Â°

â‡’ x = 180Â° â€“ 130Â° = 50Â°

## 2. Find the measure of each exterior angle of a regular polygon of

(i) 9 sides (ii) 15 sides Solution:

Sum of angles a regular polygon having side n = (n-2)Ã—180Â°

(i) Sum of angles a regular polygon having side 9 = (9-2)Ã—180Â°= 7Ã—180Â° = 1260Â°

Each interior angle=1260/9 = 140Â°

Each exterior angle = 180Â° â€“ 140Â° = 40Â°

Or,

Each exterior angle = sum of exterior angles/Number of angles = 360/9 = 40Â°

(ii) Sum of angles a regular polygon having side 15 = (15-2)Ã—180Â°

= 13Ã—180Â° = 2340Â°

Each interior angle = 2340/15 = 156Â°

Each exterior angle = 180Â° â€“ 156Â° = 24Â°

Or,

Each exterior angle = sum of exterior angles/Number of angles = 360/15 = 24Â°

## Each exterior angle = sum of exterior angles/Number of angles

24Â°= 360/ Number of sides

â‡’ Number of sides = 360/24 = 15

Thus, the regular polygon has 15 sides.

## 4. How many sides does a regular polygon have if each of its interior angles is 165Â°? Solution:

Interior angle = 165Â°

Exterior angle = 180Â° â€“ 165Â° = 15Â°

Number of sides = sum of exterior angles/ exterior angles

â‡’ Number of sides = 360/15 = 24

Thus, the regular polygon has 24 sides.

5.

a) Is it possible to have a regular polygon with measure of each exterior angle as 22Â°?

b) Can it be an interior angle of a regular polygon? Why?

Solution:

a) Exterior angle = 22Â°

Number of sides = sum of exterior angles/ exterior angle

â‡’ Number of sides = 360/22 = 16.36

No, we canâ€™t have a regular polygon with each exterior angle as 22Â° as it is not divisor of 360.

b) Interior angle = 22Â°

Exterior angle = 180Â° â€“ 22Â°= 158Â°

No, we canâ€™t have a regular polygon with each exterior angle as 158Â° as it is not divisor of 360.

## 6.

a) What is the minimum interior angle possible for a regular polygon? Why?

b) What is the maximum exterior angle possible for a regular polygon?

Solution:

a) Equilateral triangle is a regular polygon with 3 sides has the least possible minimum interior angle because the regular with minimum sides can be constructed with 3 sides at least. Since, sum of interior angles of a triangle = 180Â°

Each interior angle = 180/3 = 60Â°

b) Equilateral triangle is a regular polygon with 3 sides has the maximum exterior angle because the regular polygon with least number of sides have the maximum exterior angle possible. Maximum exterior possible = 180 â€“ 60Â° = 120Â°

Exercise 3.2 of NCERT Solutions for Class 8 Maths Chapter 3- Understanding Quadrilaterals is based on the sum of the measures of the exterior angles of a polygon. By solving these questions repeatedly, the students will improve their time management skills. By practising the solutions, the students can also increase their confidence.