Question

one exterior angle of a regular pentagon has a measure of (2x)°. what is the value of x?

x = 18
x = 20
x = 30
x = 36

Explanation:

Step1: Find the sum of exterior angles

The sum of exterior angles of any polygon is \(360^{\circ}\).

Step2: Calculate the measure of one exterior angle of a regular pentagon

For a regular pentagon (\(n = 5\)), the measure of one exterior angle is \(\frac{360^{\circ}}{n}=\frac{360^{\circ}}{5}=72^{\circ}\).

Step3: Solve for \(x\)

Given that one exterior angle is \((2x)^{\circ}\), so \(2x=72\). Then \(x = \frac{72}{2}=36\).

Answer:

\(x = 36\) (the fourth option)