In the image provided, the lines $m \parallel n$ are parallel, and a transversal $t$ intersects them. The angle of $58^\circ$ is given on the lower side of the transversal at line $n$, and we are asked to find the value of $x^\circ$, which is the angle formed between line $m$ and the transversal $t$.

Because the lines $m$ and $n$ are parallel, we can use the corresponding angles postulate. According to this rule, when a transversal crosses two parallel lines, corresponding angles are equal.

In this case, the angle of $x^\circ$ and the given angle of $58^\circ$ are corresponding angles. Thus, they are congruent.

$x = 58^\circ$

Therefore, the value of $x$ is $58^\circ$.

Would you like more details on this solution or have any further questions?

Here are 5 related questions you might consider:

1. What are alternate interior angles, and how do they relate to parallel lines?
2. How would the solution change if the given angle was on the other side of the transversal?
3. Can you prove that corresponding angles are equal when two lines are parallel?
4. What is the sum of the interior angles formed by a transversal intersecting two parallel lines?
5. How would the value of $x$ change if the lines were not parallel?

Tip: For problems involving parallel lines and transversals, always look for corresponding, alternate interior, or co-interior angles to find unknown angle measures!