In the given image, lines $l$, $m$, and $n$ are parallel, and we are tasked with finding the value of $x^\circ$.

Step-by-Step Solution:

1. Understand the setup:

   • We are told that lines $l \parallel m \parallel n$, meaning these lines are parallel to each other.
   • There is a transversal cutting through these parallel lines.
   • One of the angles formed by this transversal is 124°, and the angle labeled $x^\circ$ is adjacent to it.

2. Use the property of supplementary angles:

   • When a transversal crosses parallel lines, consecutive interior angles formed on the same side of the transversal are supplementary (i.e., their sum is 180°).
   • Here, the angle $124^\circ$ and $x^\circ$ form a linear pair (adjacent angles along a straight line), so they are supplementary.

3. Set up the equation: $x^\circ + 124^\circ = 180^\circ$

4. Solve for $x$: $x = 180^\circ - 124^\circ = 56^\circ$

Final Answer:

$x = 56^\circ$

Let me know if you'd like further clarification or have any questions.

Here are five related questions for practice:

1. What is the sum of the interior angles on the same side of the transversal?
2. If another angle on the transversal is given as 56°, what is the corresponding alternate interior angle?
3. How would the problem change if the lines were not parallel?
4. What is the relationship between corresponding angles when a transversal cuts through parallel lines?
5. How do you identify supplementary angles in a diagram with parallel lines and a transversal?

Tip: Always look for linear pairs or alternate angles when dealing with parallel lines and transversals.