**.**

**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)

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

**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

**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°

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:**

**NCERT Solutions for Maths Class 9**

**NCERT Solutions for Maths Class 10**

**NCERT Solutions for Maths Class 11**