https://file.aiquickdraw.com/mathbot/file/172658026262002syo3sk.jpg

The image shows two intersecting lines forming vertical angles. The angles are labeled as \( (5x + 4)^\circ \) and \( (8x - 71)^\circ \).

### Key Concept:
Vertical angles are always equal. Therefore, we can set the two expressions for the angles equal to each other and solve for \( x \):

\[
5x + 4 = 8x - 71
\]

### Solving the equation:

1. Subtract \( 5x \) from both sides:
   \[
   4 = 3x - 71
   \]

2. Add 71 to both sides:
   \[
   75 = 3x
   \]

3. Divide by 3:
   \[
   x = 25
   \]

### Final Answer:
The value of \( x \) is \( \boxed{25} \).

Would you like further details on this, or have any other questions?

Here are 5 related questions:
1. What are vertical angles, and why are they always equal?
2. Can you solve for \( x \) if the angles were supplementary?
3. How do we know when angles in geometry are congruent?
4. What is the relationship between complementary and supplementary angles?
5. How can you use algebra to solve angle relationships in polygons?

**Tip:** When solving angle equations, always check whether the angles are vertical, complementary, or supplementary to choose the right approach.

Find the value of x for the angles (5x + 4)° and (8x - 71)° formed by intersecting lines.

This problem involves solving for x in vertical angles formed by intersecting lines. The angles are (5x + 4)° and (8x - 71)°. The solution uses algebra and the Vertical Angles Theorem, which states that vertical angles are congruent. Suitable for students in Grades 7-9.

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