# Execise 3.2

Complete above steps to enable this content

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

(a)

**Solution:**

Three exterior angles 125°, 125° and x.

We know that, sum of the exterior angles =

Thus, 125° + 125° + x = 360°

x =

(b)

**Solution:** Our exterior angles are : x ,90°, 60°, 90°, 70°.

We know that:

Sum of exterior angles = 360°

x + 90° + 60° + 90° + 70° = 360°

x = 360° -

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

**(i) 9 sides**

**(ii) 15 sides**

**Solution:**

(i) Exterior angle =

Given: no. of sides of regular Polygon =

Exterior angle =

(ii) Exterior angle =

Given: Number of sides of regular Polygon =

Exterior angle =

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

**Solution:**

Exterior angle is 24°

In a regular polygon, sum of the exterior angles = 360°

**Exterior Angle x Number of sides = 360°**

n =

**Thus, the regular polygon has a total of 15 sides.**

Complete above steps to enable this content

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

**Solution:**

**By linear Pair:** Interior Angle + Exterior Angle = 180°

Exterior Angle =

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

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

**Solution:**

(a) In a regular polygon, sum of the exterior angles = 360°

n =

But n

**Thus, a 22° external angle measure is not possible.**

(b) By linear pair: Interior Angle + Exterior Angle = 180°.

External Angle =

In a regular polygon, sum of the exterior angles = 360°

158° x n = 360°

n =

**Since n cannot be in decimals, 158° external angle measure is not possible.**

**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) Consider a regular polygon having the least number of sides:

We know that the sum of all the angles of a triangle =

x + x + x = 180°

x =

**The minimum interior angle possible for a regular polygon is 60°.**

(b)

Consider the interior angle to be 60° since an equilateral triangle is a regular polygon having maximum exterior angle because it consists of the least number of sides.

Exterior angle = 180° -

**The maximum exterior angle possible for a regular polygon is 120°.**