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

**Solution:**

Total sum of all the exterior angles of a regular polygon = 360°

Let number of sides be = n.

Measure of each interior angle = 165°

Measure of each exterior angle = 180° - 165° = 15° [Since, an interior and an exterior angle forms a linear pair]

Number of sides = Sum of exterior angles / Each exterior angle

= 360° / 15

= 24

Hence, the regular polygon has 24 sides

**☛ Check: **NCERT Solutions for Class 8 Maths Chapter 3

**Video Solution:**

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

NCERT Solutions Class 8 Maths Chapter 3 Exercise 3.2 Question 4

**Summary:**

The number of sides a regular polygon has if the measure of an exterior angle is 165° is 24.

**☛ Related Questions:**

- (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?
- (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?
- Find the measure of each exterior angle of a regular polygon of (i) 9 sides (ii) 15 sides.
- How many sides does a regular polygon have if the measure of an exterior angle is 24°?

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