How many diagonals does a 50-sided polygon will have?

Answer 1

I have never seen this proved, but I am going to make a conjecture.:

The number of diagonals of a regular polygon of n sides is _nC₂ - n.

Let me tell you what I am thinking.

If you assign identifiers to each vertex, there are _nC₂ ways to pick 2 vertices from those points...but n of those pairs are sides. Again, I've never seen a proof and I am not able to prove my conjecture. If you get a better answer (or an answer which you can prove), I would appreciate knowing it. Thank you.