https://file.aiquickdraw.com/mathbot/file/1725488950973ebqja7fs.jpg

From the image you uploaded, I can see that it contains a diagram with two intersecting lines. One angle is marked as \(2x\), and the opposite angle is marked as \(3x + 15^\circ\).

Since these two angles are vertically opposite angles, they must be equal. So, we can set up the following equation:

\[
2x = 3x + 15^\circ
\]

### Solving the equation:

1. Subtract \(2x\) from both sides:
   \[
   0 = x + 15^\circ
   \]

2. Subtract \(15^\circ\) from both sides:
   \[
   -15^\circ = x
   \]

Thus, \(x = -15^\circ\).

Since \(x\) represents an angle, and angles cannot be negative, this result suggests that there might be additional context or constraints in the problem that we aren't accounting for.

Would you like further clarification or more details on this solution? Here are some related questions you could explore:

1. What is the significance of vertically opposite angles?
2. How do we handle negative results when solving for angle measures?
3. Are there any cases where angles can take negative values?
4. What are some real-world applications of angle relationships like vertically opposite angles?
5. Can you form other types of angles (like supplementary angles) using this diagram?

**Tip:** In geometry problems, always double-check the context of the diagram and any constraints given in the problem!

In the diagram, two intersecting lines form vertically opposite angles. One angle is labeled 2x, and the opposite angle is labeled 3x + 15°. Solve for x.

Explore how to solve for x in a geometry problem involving vertically opposite angles. Given 2x and 3x + 15°, learn the steps to find the correct angle. Suitable for students in Grades 8-10.

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