The interior angles of a polygon are in AP the smallest angle is 52 degree

CBSE Class 10
1

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

2

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.