To find the value of x, we first need to determine the measure of each exterior angle of a regular decagon. A decagon has 10 sides, and the formula to calculate the measure of each exterior angle of a regular polygon is:
Exterior Angle = 360° / n
where n is the number of sides. For a decagon (n = 10), the calculation becomes:
Exterior Angle = 360° / 10 = 36°
Now, according to the question, the measure of each exterior angle is also given as 3x – 6 degrees. We can set up the equation:
3x – 6 = 36
To solve for x, we first add 6 to both sides:
3x = 36 + 6
3x = 42
Next, we divide both sides by 3:
x = 42 / 3
x = 14
So, the value of x is 14.