To figure out how many degrees are in a pentagon we need to gather some basic information first. Note, a pentagon is a 5 sided figure. Also note, the formula for figuring out the number of degrees in a shape is (s-2) x 180, where s stands for the side. With this information we know the shape has 5 sides, so s=5. Now solve the equation. (5-2) x 180 = 540. There are 540 degrees in a pentagon.