How many diagonals are there in a polygon of n sides?

Explanation

A polygon of n sides has n vertices.
By joining any two of these vertices, we obtain either a side or a diagonal of the polygon.
Number of all straight lines obtained by joining 2 vertices at a time `=.^(n)C_(2)=(1)/(2)n(n-1)`.
These straight lines include n sides of the polygon.
Hence, the number of diagonals of the polygon
`=[(1)/(2)n(n-1)-n]=(1)/(2)n(n-3)`.