Question

1. what is the measure of each exterior angle of a regular decagon?

a) 30°
b) 36°
c) 45°
d) 60°

Explanation:

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

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

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 \(\theta=\frac{360^{\circ}}{n}\), we get \(\theta=\frac{360^{\circ}}{10}=36^{\circ}\).

Answer:

B. \(36^{\circ}\)