There are a total of 1,080 degrees in the interior of an octagon. The angles can be evenly divided into eight angles of 135 degrees, as in a regular octagon, or any random combination in an irregular octagon.
An octagon is any closed two dimensional shape with eight sides. To determine the sum of the interior angles, as many triangles as needed to completely fill the inside of the shape should be created. The triangles should be oriented so that all triangle angles coincide with at least part of an octagon angle. As there are 180 degrees in a triangle, multiplying the number of triangles needed to fill the octagon in this manner, in this case six, by 180 degrees yields the total interior degrees of an octagon: 1,080.