Are you sure this is the correct question? The smallest angle cannot be 520, because even if it is a concave polygon, there has to be angles that are acute angles. I think your question is
The interior angles of a polygon are in AP. The smallest angle is 52 degrees and the common difference is 8 degrees. Find the number of sides of the polygon.
Assume there are n sides and solve for n
Sum = n/2 [ 2a+(n-1) d]
Since the interior angles are in arithmetic progression with first term a=52 and common difference d=8,
180(n-2) = n/2 [ 2(52)+(n-1) 8]
Multiply both sides by 2
360(n-2) = n[ 104 +8n-8]
360n-720 = 104n +8n^2-8n
Rearrange the equation as a quadratic.
(n-30)(n-3) = 0
n=30 or n=3