The interior angles of a polygon are in AP the smallest angle is 52 degree and common difference is 8 degrees find no. of sides of polygon

If the smallest interior angle is 52, its corresponding exterior angle is 180-52 = 128 degrees

As the interior angles increase by 8 degrees

the corresponding exterior angles decrease by 8 degrees.

We know:

The sum of the exterior angles is 360 degrees

Let n be the number of sides. Then,

n/2 [2 x 128 + (n - 1)(-8)] = 360

Solve this equation to get the value of n, that is, the number of sides of the polygon.