Question

a. a nonagon has 27 diagonals.
b. a 15 - gon has 90 diagonals.
c. a 13 - gon has diagonals.

Explanation:

Step1: Recall diagonal - formula

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

Step2: Substitute $n = 13$

When $n = 13$, we have $d=\frac{13\times(13 - 3)}{2}$.

Step3: Simplify the expression

First, calculate $13-3 = 10$. Then, $13\times10=130$. Finally, $\frac{130}{2}=65$.

Answer:

65