The number of diagonals made in a 13-sided polygon depends on the # lines formed by connecting a vertex to all other vertices in the polygon. The rule is n-3 or 10 lines per vertex where n is number of sides of a polygon. Now, we have 13 vertices, does that mean 13*10 lines can be connected? No, we cannot get that many 13*10=130 lines crisscrossing the shape as each diagonal shares the same vertices twice. Thus the number has to be halved. Therefore, the answer is 130/2=65 diagonals.
