Number of Diagonals

There are $n$ sides if a polygon. We have to draw diagnols from one vertex. Then, we can join $n - 1$ edges with this. But $2$ sodes are the adjacent sides of the vertec od the polygon. So, the answer is $\color{#69047E}{\boxed{(n - 3)}}$ .

In a (convex) polygon of $n$ sides, there are $n-1$ points other than any one in particular and $2$ other points that are already connected to the one chosen via the existing sides, leaving $\boxed{n-3}$ possible points to draw diagonals to.