In this diagram, lines $n$ and $m$ are cut by transversals $p$ and $q$. To determine the value of $x$ that would make lines $n$ and $m$ parallel, we use the concept of corresponding angles or alternate interior angles.

For lines $n$ and $m$ to be parallel, corresponding angles or alternate interior angles created by the transversals must be equal.

Analysis:

• The 80° angle and the $x^\circ$ angle are alternate interior angles with respect to line $q$.
• For the lines $n$ and $m$ to be parallel, alternate interior angles must be equal, which means $x = 80^\circ$.

Thus, the value of $x$ that would make lines $n$ and $m$ parallel is 80°, which corresponds to option 2).

Answer:

The correct answer is 2) 80°.

Would you like further details or have any additional questions? Here are some related questions for further exploration:

1. What are corresponding angles and how are they formed by parallel lines?
2. Can transversals form supplementary angles, and how do these apply to parallel lines?
3. How would the problem change if $x^\circ$ were in a different location in the diagram?
4. How do you prove that two lines are parallel using angles formed by transversals?
5. What is the relationship between alternate exterior angles when lines are parallel?

Tip: Always look for patterns like alternate interior or corresponding angles when transversals intersect parallel lines.