each exterior angle of a regular decagon has a measure of $(3x + 6)^{circ}$. what is the value of $x$?\n$x =…

each exterior angle of a regular decagon has a measure of $(3x + 6)^{circ}$. what is the value of $x$?\n$x = 8$\n$x = 10$\n$x = 13$\n$x = 18$

each exterior angle of a regular decagon has a measure of $(3x + 6)^{circ}$. what is the value of $x$?\n$x = 8$\n$x = 10$\n$x = 13$\n$x = 18$

Answer

Explanation:

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

The sum of the exterior angles of any polygon is (360^{\circ}). For a regular decagon ((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}). So, (3x+6 = 36).

Step3: Solve the equation for (x)

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

Answer:

(x = 10)