The image shows three parallel lines labeled $l$, $m$, and $n$, with two angles formed by a transversal intersecting the parallel lines. The angles given are $(6x + 10)^\circ$ and $(9x - 8)^\circ$.

Key observations:

• Since $l \parallel m \parallel n$, the angles formed by the transversal must follow the corresponding angles or alternate interior angles properties.
• In this case, the two angles $(6x + 10)^\circ$ and $(9x - 8)^\circ$ are corresponding angles, and hence, they are equal.

Equation:

$6x + 10 = 9x - 8$

Solving the equation:

1. Subtract $6x$ from both sides: $10 = 3x - 8$

2. Add 8 to both sides: $18 = 3x$

3. Divide by 3: $x = 6$

Final answer:

The value of $x$ is $\boxed{6}$.

Would you like further clarification or details?

Here are some related questions for deeper understanding:

1. What are corresponding angles, and why are they equal for parallel lines?
2. Can alternate interior angles also be used to solve problems with parallel lines?
3. How does the transversal interact with the parallel lines to form angles?
4. Can the angles formed in this diagram be supplementary? Why or why not?
5. What other geometric properties apply when a transversal crosses multiple parallel lines?

Tip: Always check if angles formed by transversals in parallel lines are corresponding, alternate interior, or supplementary, depending on their position.