find the measure of a single exterior angle of the regular polygon shown below. if necessary, round to the…

Explanation:

Step1: Recall the formula for the measure of an exterior angle of a regular polygon

The sum of the exterior angles of any polygon is (360^{\circ}). For a regular polygon with (n) sides, the measure of a single exterior angle (E=\frac{360^{\circ}}{n}).

Step2: Determine the number of sides (n)

The given polygon is a non - agon (9 - sided polygon), so (n = 9).

Step3: Calculate the measure of the exterior angle

Substitute (n = 9) into the formula (E=\frac{360^{\circ}}{n}). So (E=\frac{360^{\circ}}{9}=40^{\circ})

Answer:

(40^{\circ})