# The Number of Sides of The Polygon is

The measure of each interior angle of a regular convex polygon is 156^{o}. The number of sides of the polygon is

- 10
- 8
- 15
- 12

**Answer: (3) 15**

**Explanation:-
**Each interior angle of a regular convex polygon = 156

^{o}

**Formula-**

The sum of interior angles = (n – 2) 180

The sum of interior angles = (n – 2) 180

**Then, the each interior angle = (n – 2) x 180/n**

**Where, n = number of the sides in the polygon.**

(n – 2) x 180/n = 156

(n – 2) x 180 = 156 x n

180 n – 360 = 156 n

180n – 156n = 360

24n = 360

n = 360 /24

n = 15

Then, the number of sides in the polygon is 15.

Hence, the answer is (3) 15.