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Class 8 NCERT Solutions – Chapter 3 Understanding Quadrilaterals – Exercise 3.2

• Last Updated : 15 Dec, 2020

Question 1. Find x in the following figures.

Solution:

As we know , the sum of the measures of the external angles of any polygon is 360Â°.

(a) 125Â° + 125Â° + x = 360Â° â‡’ 250Â° + x = 360Â° â‡’  x = 110Â°

(a) 70Â° + 60Â° + x + 90Â° + 90Â° = 360Â° â‡’ 310Â° + x = 360Â° â‡’  x = 50Â°

(i) 9 sides

Solution:

Measure of angles = 360Â°/ 9 = 40Â°

As in a regular polygon all interior angle are equal so all the exterior angles will also be equal.

(ii) 15 sides

Solution:

Measure of angles = 360Â°/ 15 = 24Â°

Question 3. How many sides does a regular polygon have if the measure of an exterior angle is 24Â°?

Solution:

Given measure of exterior angle = 24Â°

(no. of sides) x (measure of exterior angle) = 360Â° â‡’ no. of sides = 360Â°/24Â° = 15

Question 4. How many sides does a regular polygon have if each of its interior angles is 165Â°?

Solution:

Given measure of interior angle = 165Â°

measure of exterior angle = 180Â° – 165Â° = 15Â°

(no. of sides) x (measure of exterior angle) = 360Â° â‡’ no. of sides = 360Â°/15Â° = 24

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

Solution:

(a) given here, measure of exterior angle = 22Â°

As we know, (no. of sides) x (measure of exterior angle) = 360Â°

putting here value, we get

No. of sides = 360Â°/22Â° â‰ˆ 16.36 (approx), which is never possible .

Number of sides can never be fractional.

(b) No. It cannot be an interior angle of a regular polygon.

In this case , measure of exterior angle will be = 158Â°

again we will get fractional no. of sides. Hence not possible.

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

Solution:

(a) An Equilateral Triangle is a regular polygon with minimum number of sides because all sides are equal in it. We know that each angle of an equilateral triangle measures 60Â° . Hence, 60Â° is the minimum possible value for internal angle of a regular polygon.

(b) Each exterior angle of an equilateral triangle is 120Â° and hence this the maximum possible value of exterior angle of a regular polygon. This can also be proved by another principle; which states that each exterior angle of a regular polygon is equal to 360Â° divided by number of sides in the polygon. If 360Â° is divided by 3, we get 120Â° .

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