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The problem shows two angles in a vertical angle pair. Since the relationship is "vertical," we know that vertical angles are always congruent, meaning they are equal in measure.

We are given:

- One angle is \( 79^\circ \)
- The other angle is \( (5x + 4)^\circ \)

Since vertical angles are equal, we can set up the equation:

\[
79 = 5x + 4
\]

Now, let's solve for \( x \).

1. Subtract 4 from both sides:
   \[
   79 - 4 = 5x
   \]
   \[
   75 = 5x
   \]

2. Divide both sides by 5:
   \[
   x = \frac{75}{5} = 15
   \]

Thus, \( x = 15 \).

Would you like more details or further clarification?

Here are some related questions:
1. What are vertical angles and why are they always equal?
2. How would you solve if the given angles were supplementary instead of vertical?
3. Can vertical angles be obtuse or acute? Why?
4. How does the property of vertical angles apply in real-world situations, such as architecture?
5. If the second angle was given as \( (3x + 10)^\circ \), how would the process change?

**Tip:** Vertical angles are formed by two intersecting lines and are always congruent, making them useful for solving many geometry problems!

This guide explains how to solve for X using vertical angles, which are congruent. The given angles are 79° and (5x + 4)°. The solution involves solving a simple algebraic equation, making this problem suitable for students in Grades 7-9.

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