To find the value of x, we first need to remember that for any regular polygon, the measure of each exterior angle can be calculated using the formula:
Exterior Angle = 360° / n
where n is the number of sides of the polygon. In our case, since we are dealing with a regular decagon, n equals 10.
Using this formula, we calculate the measure of each exterior angle of a regular decagon:
Exterior Angle = 360° / 10 = 36°
According to the problem, each exterior angle also has a measure of 3x + 6 degrees. We can set up the following equation:
3x + 6 = 36
Now, we will solve for x:
3x + 6 = 36
First, subtract 6 from both sides:
3x = 36 – 6
3x = 30
Next, divide both sides by 3:
x = 30 / 3
x = 10
Therefore, the value of x is 10.