https://file.aiquickdraw.com/mathbot/file/1726067645685gmhk4b0d.jpg

The diagram shows two intersecting lines with angles labeled \(x + 26\) and \(3x - 32\). Since these angles are vertical angles, they are equal to each other.

We can set up the equation:

\[
x + 26 = 3x - 32
\]

Now, let's solve for \(x\):

1. Subtract \(x\) from both sides:
   \[
   26 = 2x - 32
   \]

2. Add 32 to both sides:
   \[
   58 = 2x
   \]

3. Divide by 2:
   \[
   x = 29
   \]

Thus, \(x = 29\).

Would you like more details on the solution? 

Here are some related questions:
1. What are vertical angles, and why are they equal?
2. How would you solve for \(x\) if the angles were not vertical angles?
3. Can you provide another example of a vertical angle problem?
4. What happens if the angles were supplementary instead of vertical?
5. How would you verify the solution for \(x\) is correct?

**Tip:** Always look for geometric relationships, such as vertical or supplementary angles, when solving for unknown variables in diagrams.

Solve for x given the angles: x + 26 and 3x - 32 in a vertical angle configuration.

Learn how to solve for x in a vertical angles problem with the equation x + 26 = 3x - 32. This step-by-step solution explains the use of algebra and the Vertical Angles Theorem, suitable for students in Grades 6-8.

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