https://file.aiquickdraw.com/mathbot/file/1729788177031t1ivafpj.jpg

This diagram involves two intersecting lines, which form vertical angles. Vertical angles are always congruent, meaning they are equal.

The two angles given are:

- \( (3x - 11)^\circ \) and
- \( (2x + 16)^\circ \)

Since these are vertical angles, we can set them equal to each other:

\[
3x - 11 = 2x + 16
\]

### Solving for \( x \):

1. Subtract \( 2x \) from both sides:

\[
3x - 2x - 11 = 16
\]

\[
x - 11 = 16
\]

2. Add 11 to both sides:

\[
x = 16 + 11
\]

\[
x = 27
\]

Thus, the solution is \( x = 27 \).

Let me know if you'd like further details or have any questions. 

Here are five related questions:
1. What are vertical angles?
2. How do you prove that vertical angles are congruent?
3. What is the value of each angle after solving for \( x \)?
4. How would the problem change if the angles were complementary?
5. Can this method be applied to other angle pair relationships like supplementary angles?

**Tip:** When solving equations with angles, remember that vertical angles are always equal, while supplementary angles sum to 180°.

Solve for x based on the provided diagram of intersecting lines forming vertical angles: (3x - 11)° and (2x + 16)°.

Learn how to solve for x in a problem involving intersecting lines and vertical angles: (3x - 11)° = (2x + 16)°. This geometry problem applies the Vertical Angles Theorem, suitable for students in Grades 7-9.

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