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 27 diagonals.
c. an 18 - 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 $n$ for an 18 - gon

For an 18 - gon, $n = 18$.

Step3: Substitute $n$ into the formula

Substitute $n = 18$ into $d=\frac{n(n - 3)}{2}$, we get $d=\frac{18\times(18 - 3)}{2}$.
First, calculate $18-3=15$. Then, $18\times15 = 270$. Finally, $\frac{270}{2}=135$.

Answer:

135