The sum of the exterior angles of a convex figure of any number of sides is 360 degrees. The exterior angle is measured from the extension of a side to the adjacent side. So if you start at a vertex and turn to go in the direction of the side next to you then travel to the next vertex...and so on, by the time you get back to where you started you will have turned one full circle, no more, no less.
John
My calculator said it, I believe it, that settles it