1. The problem statement, all variables and given/known data I want to show that every polygon with more than 3 sides has an interior diagonal. 2. Relevant equations 3. The attempt at a solution If the polygon is convex, this is obvious. If not, there is an interior angle at some vertex, say V, that is greater than 180 degrees. Then I think a ray emanating from V and sweeping the interior of the polygon must strike another vertex. I cannot find a counterexample to that, but I am not sure how to prove that. It seems like the polygon would be infinite if that is not true, but how can I explain that?