Question

each exterior angle of a regular decagon has a measure of $(3x + 6)^{circ}$. 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 (a polygon with \(n = 10\) sides), the measure of each exterior angle \(\theta=\frac{360^{\circ}}{n}\).
So, \(\theta=\frac{360^{\circ}}{10}=36^{\circ}\).

Step2: Set up the equation

Given that the measure of 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 \(3\): \(x=\frac{30}{3}\).

Answer:

\(x = 10\)