# 15. What is the number of sides of a regular polygon whose interior angle is of 135° each

## Answers

Answered by

7

**Number**** ****of**** ****sides**** ****:****-**** **8 Sides.

## ___________________________

### Solution

- Let the number of sides and angles of the polygon be 'n'.

- The formula for the sum S of the n interior angles of an n- sided polygon is S=(n−2)×180°

- Since the polygon is regular, all its n interior angles are the same.

Therefore the sum of them is n×135° =135n°

So, we also have S =135n°

So, setting angels equal as shown below:

**(n−2)×180° =135n**

** **

So, the regular polygon has 8 sides and is therefore, an octagon.

Similar questions