Substitute 16 (a hexadecagon has 16 sides) into the formula to find a single interior angle. If a Now you are able to identify interior angles of polygons, and you can recall and apply the formula, S = (n - 2) × 180 °, to find the sum of the interior angles of a polygon. \frac{(\red8-2) \cdot 180}{ \red 8} = 135^{\circ} $. > Sum of Interior and Exterior Angles of a Polygon + Sum of Interior and Exterior Angles of a Polygon Rating: (17) (4) (2) (6) (2) (3) ... Polygon Exterior Angles Theorem. Good luck! Award-Winning claim based on CBS Local and Houston Press awards. If each exterior angle measures 15°, how many sides does this polygon have? We still have n pairs of supplementary angles and the sum of the measures of the exterior angles is still 360°. The exterior angle theorem tells us that the measure of angle D is equal to the sum of angles A and B.In formula form: m