The degrees of a polygon, or the sum of its angles, depends on the number of sides the polygon has. The sum of the degrees of the angles of a polygon equals 180(n-2), where n equals the number of sides of the 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.