Question 71
It is considered a convex polygon having $n$ peaks, $n \geq 4$. . We arbitrarily decompose the polygon into triangles whose vertices are among the vertices of the polygon so that any two triangles have no common inner dots. We color in black the triangles that have two sides that are also sides of the polygon, with red the triangles that have exactly one side that is also the side of the polygon, and with white the triangles whose sides are not sides of the polygon. Prove that the number of black triangles is 2 greater than the number of white triangles.