How do you find diagonals in a polygon?

Suppose a polygon has n vertices (and sides). From each vertex, a diagonal can be drawn to all vertices, excluding itself and the two adjacent vertices. So n-3 diagonals can be drawn from each vertex. Multiplying by the full complement of n vertices gives n(n-3). However, as things stand we have counted each diagonal twice: once at both ends. Dividing by two gives the actual number of diagonals. number of diagonals = n(n-3)/2