https://file.aiquickdraw.com/mathbot/file/1728557522516j7ygs7tt.jpg

The image shows two intersecting lines, forming vertically opposite angles. These angles are labeled as algebraic expressions: \( 13x - 41 \) and \( 11x + 5 \). 

Since the angles are vertically opposite, they are congruent (equal). Thus, we can set up the equation:

\[
13x - 41 = 11x + 5
\]

### Solving the equation:

1. Subtract \( 11x \) from both sides to simplify:
   \[
   13x - 11x - 41 = 5
   \]
   \[
   2x - 41 = 5
   \]

2. Add 41 to both sides:
   \[
   2x = 46
   \]

3. Divide both sides by 2:
   \[
   x = 23
   \]

Thus, the value of \( x \) is 23.

Would you like more details on how to verify or apply this solution?

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Here are 5 related questions:

1. What is the value of each angle when \( x = 23 \)?
2. How do vertically opposite angles help in solving this problem?
3. Can you explain the properties of angles formed by intersecting lines?
4. What would happen if we were given supplementary angles instead?
5. How do you solve systems of equations involving multiple angles?

**Tip:** Always remember that vertically opposite angles are equal when two lines intersect. This is a key property in geometry!

Find the value of x given the vertically opposite angles represented by 13x - 41 and 11x + 5.

Learn how to solve for x in vertically opposite angles given by the expressions 13x - 41 and 11x + 5. This geometry and algebra problem covers linear equations and angle properties, suitable for students in Grades 7-9.

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