Find the number of diagonals that can be drawn in an n-side polygon

[fork]

Find the number of diagonals that can be drawn in an n-side polygon.

The answer is n(n-3)/2.

I don't know how to do that.

 

[Tide]

Set up a recursion for the number of diagonals in an n-gon: $D_{n+1} = D_n + n - 2$.

 

[fork]

I don't understand how can I set up
$D_{n+1} = D_n + n - 2$.

 

[HallsofIvy]

How many diagonals can be drawn from 1 vertex? If you multiply that by the number of vertices you will get the wrong answer! Do you see why? How can you fix it?