To answer each part of the question based on the diagram provided:

(a) Four sets of corresponding angles:

Corresponding angles are equal and are located in matching corners when a transversal crosses two parallel lines.

1. Angle 1 at line XY corresponds to Angle 1 at line NM.
2. Angle 2 at line XY corresponds to Angle 2 at line NM.
3. Angle 3 at line XY corresponds to Angle 3 at line NM.
4. Angle 4 at line XY corresponds to Angle 4 at line NM.

(b) Two sets of alternate angles:

Alternate angles are equal and lie on opposite sides of the transversal.

1. Angle 1 at line XY and Angle 3 at line NM.
2. Angle 2 at line XY and Angle 4 at line NM.

(c) Two sets of co-interior angles:

Co-interior angles are supplementary (their measures add up to 180°) and lie on the same side of the transversal.

1. Angle 1 at line XY and Angle 4 at line NM.
2. Angle 2 at line XY and Angle 3 at line NM.

Would you like further details or clarification on any part?

Related Questions

1. What are the properties of corresponding angles in parallel lines?
2. How do you identify alternate angles in a transversal?
3. Can you explain why co-interior angles are supplementary?
4. How does the concept of parallel lines affect angle relationships?
5. How would these relationships change if the lines were not parallel?

Tip:

When working with angles formed by a transversal, remember the "F", "Z", and "C" shapes to identify corresponding, alternate, and co-interior angles, respectively.