https://file.aiquickdraw.com/mathbot/file/1725856846598e93x9p2a.jpg

To solve for the value of \( x \), let's analyze the image.

The image shows two intersecting lines forming vertical angles. The angles labeled are:

- \( (3x - 7)^\circ \)
- \( 101^\circ \)

Vertical angles are congruent, meaning they are equal to each other. Therefore, we can set up the equation:

\[
3x - 7 = 101
\]

Now, solve for \( x \):

1. Add 7 to both sides:
   \[
   3x = 108
   \]

2. Divide by 3:
   \[
   x = 36
   \]

So, the value of \( x \) is 36.

Would you like more details on any step, or do you have further questions?

### Related Questions:
1. How do vertical angles relate to each other?
2. What is the definition of vertical angles?
3. How do you solve a linear equation in one variable?
4. What other properties do intersecting lines have?
5. Can you solve for \( x \) if given an equation with fractions?

### Tip:
When dealing with angles, remember that vertical angles are always equal, which can simplify solving equations quickly.

Solve for the value of x. The image shows two intersecting lines forming vertical angles. The angles labeled are: (3x - 7)° and 101°.

Learn how to solve for x using vertical angles with a step-by-step solution. This problem involves algebraic manipulation and the Vertical Angles Theorem, suitable for students in Grades 7-9.

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