To solve the problem:

Given:

• $l \parallel m \parallel n$, meaning the lines are parallel.
• Angles provided: $(2x + 20)^\circ$ and $54^\circ$.

Reasoning:

1. Since $l \parallel m \parallel n$, the angle pair $(2x + 20)^\circ$ and $54^\circ$ are corresponding angles.
2. Corresponding angles are equal when lines are parallel. Therefore: $2x + 20 = 54$

Solve for $x$:

$2x = 54 - 20$ $2x = 34$ $x = \frac{34}{2}$ $x = 17$

Final Answer:

$x = 17$

Would you like me to explain any step in more detail?

Here are 5 related questions to deepen understanding:

1. What are corresponding angles, and why are they equal in parallel lines?
2. How do we identify alternate interior angles in a similar setup?
3. What happens if the lines are not parallel? How do angle relationships change?
4. Can you generalize the equation for angles involving a transversal with parallel lines?
5. What other types of angle relationships exist with a transversal, such as supplementary angles?

Tip: Always check the diagram to identify the relationship between the angles before writing equations.