Question

Which diagram shows parallel lines cut by a transversal?

2 lines are cut by a transversal. At the intersection of the first line with the transversal, the uppercase left angle is 75 degrees. At the intersection of the second line with the transversal, the uppercase left angle is 80 degrees.

2 lines are cut by a transversal. At the intersection of the first line with the transversal, the bottom left angle is 85 degrees. At the intersection of the second line with the transversal, the uppercase right angle is 81 degrees.

2 lines are cut by a transversal. At the intersection of the first line with the transversal, the bottom right angle is 130 degrees. At the intersection of the second line with the transversal, the uppercase right angle is 50 degrees.

Answer 1

Only the third diagram.

Reasoning:
- Diagram 1: the two “upper-left” angles are corresponding; for parallel lines corresponding angles must be equal, but 75° ≠ 80°, so not parallel.
- Diagram 2: the angles are alternate interior; for parallel lines alternate interior angles must be equal, but 85° ≠ 81°, so not parallel.
- Diagram 3: the two angles (130° and 50°) are same-side (consecutive) interior angles and 130° + 50° = 180°, so they are supplementary — which implies the lines are parallel.