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

3

Explanation

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