Question

question 4 of 10
to the nearest degree, what is the measure of each exterior angle of a regular decagon?
a. 51°
b. 36°
c. 45°
d. 30°

Explanation:

Step1: Recall exterior - angle formula

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

Step2: Identify the number of sides of a decagon

A decagon has $n = 10$ sides.

Step3: Calculate the measure of each exterior angle

Substitute $n = 10$ into the formula: $\theta=\frac{360^{\circ}}{10}=36^{\circ}$.

Answer:

B. $36^{\circ}$