How many diagonals are there in a 50-sided polygon?
The number of diagonals of an n-sided polygon is:
It is very immediate to understand: from any vertex, you can draw diagonals to every other vertex, except three: the vertex itself, and the one immediately before and after.
So, for each of the
Nevertheless, you're counting each diagonal twice in this process, so you divide by two to get to the final formula.
So, you have