NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2

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

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 are the part of NCERT Solutions for Class 8 Maths (Rationalised Contents). Here you can find the NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2.

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

### Ex 3.2 Class 8 Maths Question 1.

Find x in the following figures.
Solution:
(a) Sum of all the exterior angles of a polygon = 360°
125° + 125° + x = 360°
250° + x = 360°
x = 360° – 250° = 110°
Hence, x = 110°
(b) Here,
y = 180° – 90° = 90°

and z = 90°   (given)

Sum of all the exterior angles of a polygon = 360°

x + y + 60° + z + 70° = 360°

x + 90° + 60° + 90° + 70° = 360°
x + 310° = 360°
x = 360° – 310° = 50°
Hence, x = 50°

### Ex 3.2 Class 8 Maths Question 2.

Find the measure of each exterior angle of a regular polygon of
(i) 9 sides             (ii) 15 sides

Solution:
(i) Sum of all the exterior angles of a polygon = 360°
Measure of each angle of 9-sided regular polygon = 360/9 = 40°
(ii) Sum of all the exterior angles of a polygon = 360°
Measure of each angle of 15-sided regular polygon = 360/15 = 24°

### Ex 3.2 Class 8 Maths Question 3.

How many sides does a regular polygon have if the measure of an exterior angle is 24°?

Solution:
Sum of all the exterior angles of a regular polygon = 360°
Number of sides

Hence, the number of sides in the regular polygon is 15.

### Ex 3.2 Class 8 Maths Question 4.

How many sides does a regular polygon have if each of its interior angles is 165°?

Solution:
Let n be the number of sides of a regular polygon.
Sum of all the interior angles of a polygon = (n – 2) × 180°
and, measure of its each angle

Hence, the number of sides in the regular polygon is 24.

### Ex 3.2 Class 8 Maths Question 5.

(a) Is it possible to have a regular polygon with measure of each exterior angle as 22°?
(b) Can it be an interior angle of a regular polygon? Why?

Solution:
(a) Since the sum of all the exterior angles of a regular polygon is 360°, which is not divisible by 22°.
So, it is not possible to have a regular polygon with measure of each exterior angle as 22°.

(b) Sum of all interior angles of a regular polygon with side n = (n – 2) × 180°

The value of n is not a whole number.
Since number of sides cannot be in fractions.
It is not possible for a regular polygon to have its interior angle as 22°.

### Ex 3.2 Class 8 Maths Question 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) Sum of all interior angles of a regular polygon with side n = (n – 2) × 180°
The measure of each interior angle

Therefore, the minimum number of sides in a regular polygon is 3.
The minimum measure of the angle of an equilateral triangle = 180°/3 = 60°.
(b) From part (a) we can conclude that the maximum exterior angle of a regular polygon = 180° – 60° = 120°.

Related Links:

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NCERT Solutions for Maths Class 12

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