In this image, we have two parallel lines $m \parallel n$ and a transversal $t$ intersecting both lines. You are asked to find the value of $x$, which is the angle formed at the intersection of the transversal with the line $m$.

Step-by-Step Solution:

1. Corresponding Angles: Since $m \parallel n$ and $t$ is a transversal, the angle $x^\circ$ and the angle $130^\circ$ are supplementary interior angles on the same side of the transversal. This means: $x + 130^\circ = 180^\circ$

2. Solve for $x$: Rearranging the equation: $x = 180^\circ - 130^\circ$ $x = 50^\circ$

Final Answer:

$x = 50^\circ$

Would you like more details on any step or further explanation?

Related Questions:

1. How are corresponding angles defined when two lines are parallel?
2. Can you explain the concept of alternate interior angles?
3. What are the different types of angles formed by a transversal intersecting two parallel lines?
4. How can we prove that the sum of supplementary angles is always $180^\circ$?
5. What happens if the two lines $m$ and $n$ were not parallel? How would the angles change?

Tip: Remember that when two parallel lines are cut by a transversal, corresponding angles are always equal, and alternate interior angles are also congruent.