Question

each exterior angle of a regular decagon has a measure of (3x + 6)°. what is the value of x?
○ x = 8
○ x = 10
○ x = 13
○ x = 18

Explanation:

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

The sum of exterior angles of any polygon is \(360^{\circ}\). For a regular decagon (\(n = 10\)), the measure of each exterior angle \(E=\frac{360^{\circ}}{n}\). So, \(E=\frac{360^{\circ}}{10}=36^{\circ}\).

Step2: Set up the equation

Since each exterior angle is \((3x + 6)^{\circ}\), we set \(3x+6 = 36\).

Step3: Solve the equation for \(x\)

Subtract \(6\) from both sides: \(3x=36 - 6\), so \(3x=30\).
Divide both sides by \(3\): \(x=\frac{30}{3}=10\).

Answer:

\(x = 10\) (the second option)