Question

how many diagonals does an octagon have?
_________ diagonals

Explanation:

Step1: Recall the formula for the number of diagonals

The formula for the number of diagonals \(d\) in an \(n -\)sided polygon is \(d=\frac{n(n - 3)}{2}\).

Step2: Substitute \(n = 8\) (since an octagon has \(n=8\) sides)

Substitute \(n = 8\) into the formula: \(d=\frac{8\times(8 - 3)}{2}\).
First, calculate \(8-3=5\). Then, \(8\times5 = 40\). Finally, \(\frac{40}{2}=20\).

Answer:

20