The interior angles of a convex polygon are in A.P. If the smallest angle is 100° and the common difference is 4°, then the number of sides is

We know that the sum of the interior angles of a convex polygon of n sides is (n–2) (180°). We are given a=100 and d=4.∴ n2[2(100)+(n−1)(4)]=(n−2)(180)⇒     n2−41n+180=0 ⇒ n=5,36If n=36, then interior angles of the polygon are 100°, 104°, .........,176°, 180°, 184°,......244°.