In trying to nail down an accurate definition of the external angles of a polygon, I run into this difficulty: To me, there are two external angles at each vertex, each created by extending one of the two sides that meet there.
So, are there not 2n external angles for an n-gon? Don't they really add to 720? When the textbooks say they add to 360, they only seem to count one at each vertex. Typically this is shown as the angles going around the polygon in one direction. When I try to explain it this way, I get a truly ugly definition that simply doent sound right.