Property of nonconvex polygons

Question

How to prove that each non-convex polygon with no self-intersecting parts, has at least one interior angle which size is less then $180$ degrees.

Answer 1

Hint: Consider the vertex with the largest $x$-coordinate.

Answer 2

The formula for the sum of the angles of a polygon, as a function of the number of sides, holds for non-convex as well as for convex polygons, and the result follows immediately from that formula.