How many diagonals does a polygon with 8 sides have?

The correct answer is Option (3) → 20

From each vertex of an \(n\)-sided polygon, diagonals go to all vertices except itself and its two neighbours, that is to \(n-3\) vertices. Each diagonal is counted twice, so the number of diagonals is \(\displaystyle\frac{n(n-3)}{2}\).

• Here \(n=8\)

• Number of diagonals \(\displaystyle=\frac{8\times(8-3)}{2}=\frac{8\times5}{2}=20\)