To solve for [tex]\( x \)[/tex] in the given problem, we will follow these steps:
1. Understand the geometry of the problem:
- A regular decagon is a polygon with 10 sides.
- For any regular polygon, the measure of each exterior angle is calculated by dividing 360° by the number of sides.
2. Calculate the measure of each exterior angle of a decagon:
- Since a decagon has 10 sides, each exterior angle of a regular decagon is:
[tex]\[
\frac{360^\circ}{10} = 36^\circ
\][/tex]
3. Set up the given equation:
- According to the problem, each exterior angle is given by the expression [tex]\( (3x + 6)^\circ \)[/tex].
4. Equate the two expressions for the exterior angle:
[tex]\[
3x + 6 = 36
\][/tex]
5. Solve for [tex]\( x \)[/tex]:
- Subtract 6 from both sides of the equation:
[tex]\[
3x = 36 - 6
\][/tex]
- Simplify the right side:
[tex]\[
3x = 30
\][/tex]
- Divide both sides by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{30}{3} = 10
\][/tex]
Thus, the value of [tex]\( x \)[/tex] is [tex]\( 10 \)[/tex]. The correct answer is:
[tex]\[ x = 10 \][/tex]
