At each vertex of a polygon there is both an interior and exterior angle corresponding to the angles on the inside and outside of the closed figure. When the sides of a pentagon are stretched the angles produced outside the pentagon with its sides. Image Result For Polygon Interior Angles Regular Polygon Exterior Angles Math Charts The theorem can be used to find the measure of an unknown angle in a triangleTo apply the theorem we first need to identify the exterior angle. . The angle on the outside of a polygon between a side and the extended adjacent side. A regular decagon has all sides of equal length and each internal angle will always be equal to 144. Problems in Real-World Contexts - Problem 6 Dengue Fever. Therefore the exterior angles measure 72 each. In a triangle an exterior angle is the sum of its two remote interior angles. Its interior angles add up to 3 180 540 And when it is regular all angles the same then