How Many Degrees Are in a Polygon?

A rectangle has four sides, so the sum of its angles is equal to 180(4-2), or 360 degrees. A pentagon has five sides, so the sum of its angles is equal to 180(5-2), or 540 degrees. This formula works for both regular and irregular polygons, no matter how many sides are involved. To find the measure of the angles of a regular polygon, simply apply the formula and divide by the number of sides. For example, 540 divided by 5 is 108, so the angles of a regular pentagon must each measure 108 degrees.