Question

find the measure of an exterior angle of a regular nonagon (9 - sided polygon). exterior angle = ?°

Explanation:

Step1: Recall exterior - angle formula

The sum of exterior angles of any polygon is $360^{\circ}$. For a regular polygon with $n$ sides, the measure of each exterior angle $\theta$ is given by $\theta=\frac{360^{\circ}}{n}$.

Step2: Substitute $n = 9$

Since the non - agon has $n = 9$ sides, we substitute $n$ into the formula: $\theta=\frac{360^{\circ}}{9}$.

Step3: Calculate the value

$\frac{360}{9}=40$.

Answer:

$40$