Question

a. a nonagon has 27 diagonals.
b. a 15 - gon 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 the value of $n$ for a 15 - gon

For a 15 - gon, $n = 15$.

Step3: Substitute $n$ into the formula

Substitute $n=15$ into $d=\frac{n(n - 3)}{2}$, we get $d=\frac{15\times(15 - 3)}{2}$.
First, calculate $15-3 = 12$. Then, $15\times12=180$. Finally, $\frac{180}{2}=90$.

Answer:

90