Proof Writing & Problem Solving · Medium problem

Strong induction shows that any way of cutting a convex $n$-gon into triangles by non-crossing diagonals uses exactly $n - 2$ triangles (a first diagonal splits it into a $(k+1)$-gon and an $(n-k+1)$-gon). How many diagonals does such a triangulation of a convex $15$-gon use?