The interior angles of a polygon are in AP. The smallest angle is 520 and the common difference is 80. Find the number of sides of the polygon.
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