https://file.aiquickdraw.com/mathbot/file/1728487110148duc9bcy0.jpg

From the image provided, it appears that you are asked to solve for \( x \) given the angles formed by intersecting lines.

The given information includes:
- Angle \( \angle PVS = (15x + 8)^\circ \)
- Angle \( \angle TWU = (9x + 26)^\circ \)

These angles are vertically opposite, meaning they are equal. We can set up the equation:

\[
15x + 8 = 9x + 26
\]

### Step-by-step solution:

1. Subtract \( 9x \) from both sides:
\[
15x - 9x + 8 = 26
\]
\[
6x + 8 = 26
\]

2. Subtract 8 from both sides:
\[
6x = 18
\]

3. Divide by 6:
\[
x = 3
\]

Thus, \( x = 3 \).

Would you like more details on any part of the process, or do you have further questions?

### Related questions:
1. What are vertically opposite angles, and why are they equal?
2. How would the problem change if the lines were not intersecting?
3. Can you provide other examples of solving for \( x \) with different angle relationships?
4. What are alternate interior angles, and how are they used in geometry?
5. Can you verify the solution by plugging \( x = 3 \) back into the original expressions?

### Tip:
When solving equations with angles, always check if they are complementary, supplementary, or vertically opposite for helpful relationships!

Solve for x given that angle PVS = (15x + 8) degrees and angle TWU = (9x + 26) degrees, where the angles are vertically opposite.

Learn how to solve for x in a problem involving vertically opposite angles. The solution involves setting up a linear equation using the given angle expressions (15x + 8)° and (9x + 26)°. Suitable for students in Grades 8-10.

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