# Understanding Quadrilaterals : Exercise 3.2 (Mathematics NCERT Class 8th)

**Q.1 Find x in the following figures.**

**(a) We know that the sum of all exterior angles of any polygon is 360áµ’**

*Sol.*Hence, 125áµ’ + 125áµ’ +

*x*= 360áµ’

250áµ’ +

*x*= 360áµ’

*x*= 110áµ’

(b) We know that the sum of all exterior angles of any polygon is 360áµ’

Hence, 60áµ’ + 90áµ’ + 70áµ’ + *x + *90áµ’ = 360áµ’

310áµ’ + *x *= 360áµ’

*x *= 50áµ’

**Q.2 Find the measure of each exterior angle of a regular polygon of
**

**(i) 9 sides (ii) 15 sides**

**(i) We know that the sum of all exterior angles of any polygon = 360áµ’**

*Sol.*For any regular polygon, the measure of each exterior angle is same.

Hence, measure of each exterior angle of a regular polygon having 9 sides =

(ii) We know that the sum of all exterior angles of any polygon = 360áµ’

For any regular polygon, the measure of each exterior angle is same.

Hence, measure of each exterior angle of a regular polygon having 15 sides =

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

**We know that the sum of all exterior angles of any polygon = 360áµ’**

*Sol.*Given, measure of an exterior angle = 24áµ’

Therefore, number of sides of the regular polygon =

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

**Let the number of sides be x.**

*Sol.*Here, the exterior angle will be (180Â° -165Â°) = 15Â°

We know that the sum of all exterior angles of any polygon = 360áµ’

Therefore, number of sides of the regular polygon =

**Q.5 (a) Is it possible to have a regular polygon with measure of each exterior angle as 22Â°?
**

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

**(a) No.**

*Sol.*It is not possible to have a regular polygon with measure of each exterior angle as 22Â°.

Reason: The sum of all exterior angles of any polygon is 360áµ’. Hence, each exterior angle has to be multiple of 360áµ’.

Here, 22Â° is not the multiple of 360áµ’ and hence such polygon is not possible.

(b) No.

It is not possible to have a regular polygon with measure of interior angle as 22Â°.

Reason: The sum of all exterior angles of any polygon is 360áµ’. Hence, each exterior angle has to be multiple of 360áµ’.

Here, interior angle = 22Â°

Therefore, exterior angle = 180Â° - 22Â° = 158Â°

Here, 158Â° is not the multiple of 360áµ’ and hence such polygon is not possible.

**Q.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?**

**(a) A regular polygon with lowest possible number of equal sides is 3 (i.e. equilateral triangle) which is 60áµ’**

*Sol.*Since, sum of all the angles of a triangle = 180áµ’

Hence, x + x + x = 180áµ’

3x = 180áµ’

x = 60áµ’

Hence, minimum interior angle possible for a regular polygon is 60áµ’.

(b) A regular polygon with lowest possible number of sides is 3.

We know that the sum of all exterior angles of any polygon = 360áµ’

So, exterior angle of triangle =

Hence, maximum exterior angle possible for a regular polygon is 120áµ’.