Question

find the measure of a single exterior angle of the regular polygon shown below. if necessary, round to the nearest tenth. answer attempt 1 out of 2

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 \(E=\frac{360^{\circ}}{n}\). Then \(E=\frac{360^{\circ}}{9}=40^{\circ}\)

Answer:

\(40^{\circ}\)