To solve this problem, we need to use the properties of parallel lines and the angles formed by a transversal.

Problem Analysis:

1. The lines $l$, $m$, and $n$ are parallel, and a transversal cuts across these lines.
2. The angle marked as $63^\circ$ is formed by the transversal and line $l$.
3. We need to find the value of $x^\circ$, the angle formed by the transversal and line $n$.

Solution:

Since $l \parallel m \parallel n$, the transversal creates alternate interior angles, corresponding angles, and co-interior angles.

1. The angle marked $63^\circ$ is a corresponding angle with the angle on the same side of the transversal near line $m$. Therefore, the angle formed by the transversal and line $m$ on the upper side is also $63^\circ$.

2. The angle $x^\circ$ is on the opposite side of the transversal near line $n$. Since $x^\circ$ and the previously found $63^\circ$ angle are alternate interior angles, they are congruent.

Thus, $x = 63^\circ.$

Final Answer:

$x = 63^\circ.$

Would you like further details or have any questions?

Here are some related questions you might consider:

1. What are alternate interior angles, and how do they relate to parallel lines?
2. How can we determine corresponding angles in parallel lines cut by a transversal?
3. What other types of angle relationships exist in parallel line configurations?
4. How do co-interior angles help in solving for unknown angles?
5. How do the properties of transversals help in real-life applications?

Tip: Always look for corresponding and alternate interior angles when dealing with parallel lines cut by a transversal.