In this problem, we are dealing with two parallel lines, $m \parallel n$, cut by a transversal line $t$. The diagram shows a 13° angle and an unknown angle $x$, and we are asked to find the value of $x$.

Step-by-step solution:

1. Recognize the relationship between angles:

   • Since $m \parallel n$ and $t$ is the transversal, we know that corresponding angles are equal.
   • The 13° angle and the $x$° angle are corresponding angles because they are in the same relative position (on opposite sides of the transversal, but both on the same side of the parallel lines).

2. Set up the equation:

   • Since corresponding angles are equal, we have: $x = 13^\circ$

Thus, the value of $x$ is $13^\circ$.

Would you like more details or have any questions about this problem?

5 Related Questions:

1. What are alternate interior angles, and how can they help in similar problems?
2. How do you calculate angles when the lines are not parallel?
3. What are vertical angles, and how are they related to transversal problems?
4. What other angle relationships exist when two parallel lines are cut by a transversal?
5. How would the solution change if $m$ and $n$ were not parallel?

Tip:

In problems involving parallel lines and a transversal, always look for relationships like corresponding, alternate interior, and alternate exterior angles, as they often provide a direct solution.