Angle sum theorem states the total degrees in a polygon on adding all the interior angles of that polygon. The geometric figure in which the angle sum theorem is most predominantly used is the triangle. A triangle is a three sided figure having three edges and three vertices. Triangle angle sum theorem states that the three interior angles of the triangle add up to 180 degrees. Angle sum theorem is used in many algebra and geometry problems. It is mostly used to find out the unknown angle in a triangle or in the exterior angle theorem or even in the polygon angle sum formula.