Question

determine how many diagonals each of the following polygons has. a. heptagon b. nonagon a. a heptagon has 14 diagonals. b. a nonagon has diagonals.

Explanation:

Step1: Recall the diagonal - formula

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

Step2: Identify $n$ for non - agon

A non - agon has $n = 9$ sides.

Step3: Substitute $n$ into the formula

Substitute $n = 9$ into $d=\frac{n(n - 3)}{2}$, we get $d=\frac{9\times(9 - 3)}{2}=\frac{9\times6}{2}$.

Step4: Calculate the result

$\frac{9\times6}{2}=27$.

Answer:

27