Does anyone know of a theorem or equation that will determine how many diagonals a polygon has, without having to do a drawing to see how many there are?

Dec 23, 2015

$n \times \frac{n - 3}{2}$

where, n is the number of sides

Explanation:

For example ...

triangle: $3 \times \frac{3 - 3}{2} = 0$ diagonals

pentagon: $5 \times \frac{5 - 3}{2} = 5$ diagonals

hope that helped