Punjab State Board PSEB 8th Class Maths Book Solutions Chapter 3 Understanding Quadrilaterals Ex 3.2 Textbook Exercise Questions and Answers.

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

Question 1.

(a)

Solution:

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

∴ x + 125° + 125° = 360°

∴ x + 250° = 360°

∴ x = 360° – 250° (Transposing 250° to RHS)

∴ x = 110°

(b)

Solution:

In this figure, two exterior angles are of 90° each. (one interior angle is 90°)

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

∴ x + 90° + 60° + 90° + 70° = 360°

∴ x + 310° = 360°

∴ x = 360° – 310° (Transposing 310° to RHS)

∴ x = 50°

Question 2.

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

Solution:

(i) Number of sides (n) = 9

∴ Number of exterior angles = 9

The sum of all exterior angles = 360°.

The given polygon is a regular polygon.

∴ All the exterior angles are equal.

∴ Measure of an exterior angle = \(\frac{360^{\circ}}{9}\).

= 40°

(ii) Number of sides of regular polygon = 15

∴ Number of exterior angles = 15

The sum of all the exterior angles = 360°

The given polygon is a regular polygon.

∴ All the exterior angles are equal.

∴ The measure of each exterior angle = \(\frac{360^{\circ}}{15}\) = 24°

Question 3.

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

Solution:

Regular polygon is equiangular.

Sum of all the exterior angles = 360°

Measure of an exterior angle = 24°

∴ Number of sides = \(\frac{360^{\circ}}{24^{\circ}}\)

The polygon has 15 sides.

Question 4.

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

Solution:

The given polygon is regular polygon.

Each interior angle = 165°

∴ Each exterior angle = 180° – 165° = 15°

∴ Number of sides = \(\frac{360^{\circ}}{15^{\circ}}\) = 24

The polygon has 24 sides.

Question 5.

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

Solution:

Each exterior angle = 22°

∴ Number of sides = \(\frac{360^{\circ}}{22^{\circ}}=\frac{180^{\circ}}{11^{\circ}}\)

The number of sides of a regular polygon must be a whole number.

But, \(\frac {180}{11}\) is not a whole number.

∴ No, exterior angle of a regular polygon cannot be of measure 22°.

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

Solution:

If the measure of an interior angle of a polygon is 22°, then the measure of its exterior angle = 180° – 22° = 158°.

∴ Number of sides = \(\frac{360^{\circ}}{158^{\circ}}=\frac{180^{\circ}}{79^{\circ}}\)

\(\frac {180}{79}\)is not a whole number.

∴ No, 22° cannot be an interior angle of a regular polygon.

Question 6.

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

Solution:

The minimum number of sides of a polygon = 3

The regular polygon of 3-sides is an equilateral triangle.

Each interior angle of an equilateral triangle = 60°.

Hence, the minimum possible interior angle of a polygon = 60°.

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

Solution:

The sum of an exterior angle and its corresponding interior angle is 180°. (Linear pair)

And minimum interior angle of a regular polygon = 60°.

∴ The maximum exterior angle of a regular polygon = 180° – 60° = 120°.