https://file.aiquickdraw.com/mathbot/file/1729871933747b32j5992.jpg

To solve this problem, we need to find the value of \( x \) based on the angles shown in the diagram.

### Step-by-Step Solution:

1. **Understanding the Diagram**:
   - Two intersecting lines are shown, forming vertical angles.
   - One angle is \( 118^\circ \), and its vertical angle is labeled \( (8x + 6)^\circ \). Since vertical angles are equal, we can set these two angles equal to each other.

2. **Setting up the Equation**:
   \[
   (8x + 6)^\circ = 118^\circ
   \]

3. **Solving for \( x \)**:
   - First, subtract 6 from both sides:
     \[
     8x = 118 - 6
     \]
     \[
     8x = 112
     \]
   - Now, divide both sides by 8:
     \[
     x = \frac{112}{8} = 14
     \]

Thus, the value of \( x \) is \( 14 \).

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Would you like more details or have any other questions?

Here are some related questions you could explore:
1. What are vertical angles, and why are they equal?
2. How would the equation change if the given angle was different from \( 118^\circ \)?
3. How do you verify that the solution for \( x \) is correct?
4. What are some other properties of intersecting lines that can be useful in geometry?
5. Could you solve for \( x \) if the angles were supplementary instead of equal?

**Tip:** Always double-check your algebra steps to avoid errors when solving equations.

Complete the steps to find the value of x based on the angles shown in the diagram.

Learn how to solve for x using vertical angles and basic algebra. The problem involves setting up an equation based on congruent vertical angles, simplifying the equation, and solving for the unknown x. Suitable for students in Grade 8-10.

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