Counting the number of internal intersection points made by the diagonals of irregular convex polygons where no three diagonals are concurrent is an interesting problem in discrete mathematics. This paper uses an iterative approach to develop a summation relation which tallies the total number of intersections, and shows that this total can be expressed as a simple sum of products. This iterative approach also motivates solutions for the number of internal regions and number of line segments produced by the diagonals.