The problem involves three parallel lines $l \parallel m \parallel n$ and a transversal that forms an angle $x^\circ$ with line $l$ and a $49^\circ$ angle with line $n$. We need to determine the value of $x$.

Solution:

1. Understand the Parallel Lines and Angles:

   • When a transversal intersects parallel lines, corresponding angles are equal.
   • Here, since $l \parallel m \parallel n$, the angles formed with the transversal will be equal due to corresponding angle relationships.

2. Identify Corresponding Angles:

   • The angle of $49^\circ$ given at the intersection with line $n$ is corresponding to the angle $x$ at line $l$.
   • Thus, $x^\circ$ and $49^\circ$ are corresponding angles.

3. Set Up the Equation:

   • Since corresponding angles are equal: $x = 49^\circ$

Final Answer:

$x = 49^\circ$

Would you like further details or have any questions? Here are a few related questions for further practice:

1. What is the relationship between alternate interior angles when a transversal intersects parallel lines?
2. How do you find the value of angles when two parallel lines are cut by a transversal and a supplementary angle is given?
3. If the transversal forms angles of $60^\circ$ with one line, what will be the corresponding angle on a parallel line?
4. How do you determine angles when parallel lines are cut by a transversal forming alternate exterior angles?
5. What are the properties of corresponding angles when a transversal cuts through three parallel lines?

Tip: When working with parallel lines and transversals, remember that corresponding angles, alternate interior angles, and vertically opposite angles are key relationships to identify.