Let's solve the problem step by step:
### Step 1: Understanding the Problem
- We have a regular decagon, which is a polygon with 10 sides.
- We are given that each exterior angle of this regular decagon is [tex]\((3x + 6)^\circ\)[/tex].
- We need to find the value of [tex]\(x\)[/tex].
### Step 2: Calculate the Measure of Each Exterior Angle of a Regular Decagon
- The formula for finding the measure of each exterior angle of a regular polygon with [tex]\(n\)[/tex] sides is [tex]\(\frac{360^\circ}{n}\)[/tex].
- For a decagon, [tex]\(n = 10\)[/tex].
- Thus, each exterior angle of a regular decagon is [tex]\(\frac{360^\circ}{10} = 36^\circ\)[/tex].
### Step 3: Set Up the Equation
- According to the problem, each exterior angle is also given by [tex]\((3x + 6)^\circ\)[/tex].
- We equate this to the exterior angle value we calculated: [tex]\[ 3x + 6 = 36 \][/tex]
### Step 4: Solve for [tex]\(x\)[/tex]
- To solve for [tex]\(x\)[/tex], first subtract 6 from both sides: [tex]\[ 3x = 36 - 6 \][/tex]
- Simplify the right-hand side: [tex]\[ 3x = 30 \][/tex]
- Divide both sides by 3: [tex]\[ x = \frac{30}{3} = 10 \][/tex]
### Conclusion
- Hence, the value of [tex]\(x\)[/tex] is [tex]\(10\)[/tex].
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(\boxed{10}\)[/tex].
