Interior Angle = Sum of the interior angles of a polygon / n, Below is the proof for the polygon interior angle sum theorem. Same thing for an octagon, we take the 900 from before and add another 180, (or another triangle), getting us 1,080 degrees. Apply the law of sines or trigonometry to find the right triangle side lengths: a = c * sin (α) or a = c * cos (β) b = c * sin (β) or b = c * cos (α) Given angle and one leg. Take any dodecagon and pick one vertex. One property of all convex polygons has to do with the number of diagonals that it has: Every convex polygon with n sides has n(n-3)/2 diagonals. In formula form: m