In this image, we see two angles formed by transversals intersecting parallel lines. The angle expressions are given as:

1. $(13x + 79)^\circ$
2. $(17x + 67)^\circ$

These two angles are corresponding angles, as they are positioned on the same side of the transversal and correspond to the two parallel lines. Corresponding angles are always equal when lines are parallel.

Thus, we set the two expressions equal to each other:

$13x + 79 = 17x + 67$

Solve for $x$:

1. Subtract $13x$ from both sides:

$79 = 4x + 67$

2. Subtract 67 from both sides:

$12 = 4x$

3. Divide both sides by 4:

$x = 3$

Thus, the value of $x$ is $3$.

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

Here are 5 related questions you might find helpful:

1. What are other types of angle pairs formed by transversals and parallel lines?
2. How can we prove two lines are parallel using angle pairs?
3. What is the significance of alternate interior angles in geometry?
4. How do we apply corresponding angles in real-world problems?
5. How can supplementary angles be used when solving for unknown variables?

Tip: When solving for unknowns in geometry, always look for relationships like parallel lines, which often result in equal or supplementary angles!