Question

The interior angles of a polygon are in AP. If the smallest angle is 120° and the common difference is 5°, then the number of sides is

(A)  8 

(B)  10 

(C)  9 

(D)  6

Answer 1

Correct option (C)  9

Let the number of sides of the polygon be n. Then the sum of interior angles of the polygon is

(2n - 4)π/2 = (n - 2)π

Since the angles are in AP and a = 120° ,d = 5, therefore

But n = 16 gives T₁₆ = a + 15d = 120° + 15.5° =195°, which is impossible as interior angle cannot be greater than 180°. Hence, n = 9.