Gujarat Board GSEB Textbook Solutions Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Textbook Questions and Answers.

### Gujarat Board Textbook Solutions Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2

Question 1.

Find x in the following figures.

Solution:

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

∴ 125° + 125° + x = 360°

or 250° + x = 360°

or x = 360° – 250° = 110°

(b) ∵ x + 90° + 60° + 90° + 70° = 360°

or x + 310° = 360°

or x = 360° – 310° = 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

Since, sum of all the exterior angles = 360°

∴ The given polygon is a regular polygon.

∵ All the exterior angles are equal.

∴ Measure of an exterior angle = \(\frac { 360° }{ 9 }\) = 40°

(ii) Number of sides of regular polygon =15

∴ Number of equal exterior angles =15

The sum of all the exterior angles = 360°

∴ The measure of each exterior angle

= \(\frac { 360° }{ 15 }\)

Question 3.

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

Solution:

For a regular polygon, measure of each angle is equal.

∴ Sum of all the exterior angles = 360°

Measure of an exterior angle = 24°

∴ Number of angles = \(\frac { 360° }{ 24° }\) =15

Thus, there are 15 sides of the polygon.

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 = \(\frac { 360° }{ 15° }\) = 24

Thus, there are 24 sides of the polygon.

Question 5.

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

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

Solution:

(a) Each exterior angle = 22°

Number of sides = \(\frac { 360° }{ 22° }\) = \(\frac { 180 }{ 11 }\)

If it is a regular polygon, then its number of sides must be a whole number.

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

∴ 22° cannot be an exterior angle of a regular polygon.

(b) If 22° is an interior angle, then 180° -22°, i.e., 158° is an exterior angle.

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

which is not a whole number.

Thus, 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?

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

Solution:

(a) 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) ∵ The sum of an exterior angle and its corresponding interior angle is 180°

And minimum interior angle of a regular polygon = 60°

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