The interior angles of a polygon are in AP. The smalllest angle is `52^(@)` and the common difference is `8^(@)`. Find the number of sides of the polygon.

The interior angles of a polygon are in AP. The smalllest angle is `52

1.	The interior angles of a polygon are in AP. The smalllest angle is `52^(@)` and the common difference is `8^(@)`. Find the number of sides of the polygon.
Answer» Correct Answer - 3 Let the number of sides of the polygon be n . Then , Sum of its interior angles = ` ( 2n-9) x x 90^(@) = ( 180n -360)^(@)` ` 52+ 60+68 +…..tp n terms = ( 180n - 360) ` ` Rightarrow n/2 xx [2 xx 52 + (n-1) xxn 8] = 180n -360` `Rightaarrow n^(2) -33n +90 =0 Rightarrow (n-3) (n-30) =0 Rightarrow n =3 or n=30` When n=30 ,then last angle = ` [ 52+ 29xx 8]^(@) = 284^(@)` , which is a reflex angle , So, ` n ne 30` Hence , n=3