A polygon is a closed two-dimensional shape composed of three or more connected line segments. Triangles, trapezoids and octagons are common examples of polygons. Polygons are typically classified according to number of sides and the relative measures of its sides and angles. They also are classified as regular or non-regular polygon. Regular polygons have sides of equal length and angles of equal degree. You can calculate the degrees of the angles in regular polygons but can't always do so with non-regular polygon.
Calculating the Angles
Add the number of sides of the polygon. The sum of all the degrees of the interior angles equals (n - 2)_180. This formula means subtract 2 from the number of sides and multiply by 180). For example, the sum of degrees for an octagon is (8-2)_180. This equals 1,080.
If the polygon is regular (sides and angles are all equal), divide the sum produced in Step 1 by the number of sides. This is the degree of each angle in the polygon. For example, the degree of each angle in a regular octagon is 135: Divide 1,080 by eight.
Calculate the supplement of the angle from Step 2 (180 minus the degree) to find the exterior angle measure of a regular polygon. This is the degree of every exterior angle on the polygon. In this example's case, the angle is 135, so 180 minus 135 equals 45 for the value of the supplemental angle.
If the polygon is not regular (the sides or angles are not all equal), it is much more difficult and often impossible to calculate the degrees of the individual interior angles, however, you can calculate the sum of the interior and exterior angles the same way you would with a regular polygon.