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

Hence, 125áµ’ + 125áµ’ +

250áµ’ +

(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
**

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°?
**

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°?
**

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°?
**

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?
**

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’.

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