According to the University of Washington math department, a regular pentagon has five obtuse angles. The sum of all angles for a regular pentagon is 540 degrees, making each angle 108 degrees. Any angle over 90 degrees is obtuse.
The pentagon is a flat-shaped, five-sided polygon. Irregular polygons are considered convex or concave. When an internal angle of a pentagon is greater than 180 degrees, the pentagon is concave. A convex pentagon is not going to have any internal angles that are greater than 180 degrees, and no angles point inwards as they do within a concave pentagon. If any sides are curved, the figure is not considered a polygon.