The problem from the image asks for the value of $x$ given that two lines, $l$ and $m$, are parallel. From the diagram, it seems to involve corresponding or alternate angles formed by a transversal intersecting these parallel lines.

Let’s break it down:

1. You have two parallel lines intersected by a transversal.
2. Angles labeled $(x + 13)^\circ$ and $34^\circ$ appear on opposite sides of the transversal. These angles are alternate interior angles.

Since the lines are parallel, alternate interior angles are equal. Therefore:

$x + 13 = 34$

Now, solve for $x$:

$x = 34 - 13$ $x = 21$

Thus, the value of $x$ is $\boxed{21}$.

Would you like more details or clarifications on this problem?

Here are 5 related questions:

1. What is the definition of alternate interior angles?
2. How can you identify corresponding angles in parallel lines?
3. What other angle relationships exist when a transversal intersects parallel lines?
4. How do supplementary angles help in finding unknown angles?
5. What properties of parallel lines are useful for solving angle problems?

Tip: Always look for key relationships between angles (corresponding, alternate, or supplementary) when dealing with parallel lines and transversals.