Question

When two parallel lines are cut by a transversal, which sets of angles must be supplementary?

A) Corresponding angles
B) Alternate interior angles
C) Alternate exterior angles
D) Vertical angles

Answer 1

When two parallel lines are cut by a transversal, consecutive interior angles (same side interior angles) are supplementary. The options listed did not include this, but alternate exterior angles and other listed types are equal, not supplementary.

Step-by-step explanation:

When two parallel lines are cut by a transversal, the sets of angles that must be supplementary are the alternate exterior angles and the consecutive interior angles, which are also known as same side interior angles. However, among the options provided:

1. Corresponding angles are equal, not supplementary.
2. Alternate interior angles are also equal.
3. Alternate exterior angles are equal as well.
4. Finally, vertical angles are also equal angles.

The correct answer, according to the typical relationships of angles formed by a transversal and parallel lines, would actually be 'Consecutive (same side) interior angles'. If the question meant to include that option, then consecutive interior angles are the ones that would be correct as they add up to 180 degrees and are therefore supplementary.