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

Let there be n sides of the polygon. Then, the sumof all interior angles is (2n - 4) right angles.n2{240+(n-1)5}=(2n-4)90.n2-25n+144=0⇒n=9,16But, for n=16, the largest angle =120+(16-1)5=1950which is impossible.Hence, n=9.