Hi Sofia,

If you go to the Quandaries and Queries page on Math Central
http://mathcentral.uregina.ca/QandQ/
and use the Quick Search to search for the term diagonal you will see number of questions we have received on diagonals of polygons. I am going to suggest 3 that you should look at. I suggest you look at them in the order I have given.

Julie's asked about the number of diagonals from one vertex of a 12 sided polygon. In Leeanna's response she defines a diagonal and answers Julie's question.

Karan asked about the number of diagonals in an 11 sided polygon (a hendecagon) and Penny leads Karan in a process to build on Leeanne's response above to answer her question.

Edna's question is about the number of diagonals in an $n$ sides polygon and Stephen takes an entirely different approach to answer her question.

If you want to extend Leeanne's and Penny's approach to a general formula you might want to look at our reply to Steven.

Let me know if you need any other assistance,
Harley