Gujarat BoardĀ 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 = 360Ā°

ā“ 125Ā° + 125Ā° + x = 360Ā°

or 250Ā° + x = 360Ā°

or x = 360Ā° – 250Ā° = 110Ā°

(b) āµ x + 90Ā° + 60Ā° + 90Ā° + 70Ā° = 360Ā°

or x + 310Ā° = 360Ā°

or x = 360Ā° – 310Ā° = 50Ā°

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 = 360Ā°

ā“ The given polygon is a regular polygon.

āµ All the exterior angles are equal.

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

(ii) Number of sides of regular polygon =15

ā“ Number of equal exterior angles =15

The sum of all the exterior angles = 360Ā°

ā“ The measure of each exterior angle

= \(\frac { 360Ā° }{ 15 }\)

Question 3.

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

Solution:

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

ā“ Sum of all the exterior angles = 360Ā°

Measure of an exterior angle = 24Ā°

ā“ Number of angles = \(\frac { 360Ā° }{ 24Ā° }\) =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 165Ā°?

Solution:

The given polygon is regular polygon.

Each interior angle = 165Ā°

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

Number of sides = \(\frac { 360Ā° }{ 15Ā° }\) = 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 22Ā°?

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

Solution:

(a) Each exterior angle = 22Ā°

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

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.

ā“ 22Ā° cannot be an exterior angle of a regular polygon.

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

ā“ Number of sides = \(\frac { 360Ā° }{ 158Ā° }\) = \(\frac { 180Ā° }{ 79 }\)

which is not a whole number.

Thus, 22Ā° 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.

ā“ Each interior angle of an equilateral triangle = 60Ā°

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

(b) āµ The sum of an exterior angle and its corresponding interior angle is 180Ā°

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

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