Find the number of sides:

Question

The interior angles of a polygon are in AP the smallest angle is 120 degrees and the common difference is 5 degrees. Find the number of sides of the polygon.

Answer 1

Smallest angle=120degree

Common difference=5

A P is 120, 125, 130,……..

The sum of interior angles of a polygon= (n-2)180

Hence Sum of n terms of an A P = (n-2)180

n/2 {2.120+(n-1)5} = 180(n-2)

5n^2 -125n +720 = 0

n^2 -25n +144=0

n=9 or 16

hence number of sides can be 9 or 16