The exterior angles of any convex polygon add to 360 degrees. So for a regular pentagon, the exterior angle is 360/5 = 72 degrees. The interior angle is supplementary to the exterior angle so is 180 - 72 = 108 degrees. So the sum of them is 5(108) = 540 degrees.
The formula for the sum of the interior angles of a regular polygon in degrees is , where is the number of sides on the polygon.
In the case of a regular pentagon with five sides, we can say that . Using the formula below, we can find the sum of the interior angles of the pentagon:
