To find the sum of the interior angles of a pentagon, divide it up into triangles... There are three triangles... Because the sum of the angles of each triangle is 180 degrees... We get. So, the sum of the interior angles of a pentagon is 540 degrees. Regular Pentagons: All sides are the same length (congruent) and all interior angles are the same size (congruent). To find the measure of the interior angles, we know that the sum of all the angles is 540 degrees (from above)... And there are five angles... So, the measure of the interior angle of a regular pentagon is 108 degrees.