What is the sum of the exterior angles of any convex polygon?
1 Answer
There are two exterior angles near each vertex. Let's call them "left" and "right".
The sum of all "left" exterior angels equals to the sum of all "right" ones and equals to
Explanation:
Consider we stand on the vertex of a horizontally positioned regular polygon with
Turn from that direction towards the nearest side (clockwise on the illustrative picture above) by exterior angle and move along that side towards the next vertex.
Coming to this next vertex, we extend the side we walked upon and look along this extension. The situation is similar to the one before.
Turn again from that direction towards the nearest side by exterior angle, walk along it to the next vertex, extend this side and look straight ahead.
Continuing this process
Similarly, all other exterior angles ("right" ones, when we move counterclockwise) also sum up to