If the vertices are labelled 1 to 54, and a diagonal is a line between 2 non-adjacent vertices, then there are 51 diagonals from vertex 1. There are also 51 diagonals from vertex 2. From vertex 3 there are only 50 new diagonals because we have already counted the diagonal from 1 to 3. From vertex 4 there are 49 new diagonals, and so on, until there is only 1 new diagonal from 52 to 54, every other diagonal having already been counted. So we need a formula for 51+51+50+49+48+...+2+1. The formula for the sum of natural numbers up to n is n(n+1)/2, therefore if n=51, we have 51×52/2=51×26=1326. To this we need to add 51 to give us 1377 diagonals. The general formula for an n-gon is n-3+(n-3)(n-2)/2. Note that when n=4 (quadrilateral), the number of diagonals is 1+1×2/2=2, which is correct.