Which statement describes the relationship of alternate exterior angles when two lines are parallel and cut by a transversal?

Which statement describes the relationship of alternate exterior angles when two lines are parallel and cut by a transversal?

• A. They are congruent.
• B. They are supplementary.
• C. They are perpendicular.
• D. They are vertical angles.

Answer: (A)

When two lines are parallel and a transversal cuts them, the angles outside the lines on opposite sides of the transversal have equal measures. This happens because the transversal creates corresponding angles that are equal on each intersection, and the alternate exterior pair matches those corresponding positions across the two intersections, so their measures must be the same. In other words, the tilt created by the transversal is the same at both intersections, leading to congruent alternate exterior angles. They’re not necessarily 90 degrees, not vertical angles (which are opposite at the same intersection), and not inherently supplementary.

When two lines are parallel and a transversal cuts them, the angles outside the lines on opposite sides of the transversal have equal measures. This happens because the transversal creates corresponding angles that are equal on each intersection, and the alternate exterior pair matches those corresponding positions across the two intersections, so their measures must be the same. In other words, the tilt created by the transversal is the same at both intersections, leading to congruent alternate exterior angles. They’re not necessarily 90 degrees, not vertical angles (which are opposite at the same intersection), and not inherently supplementary.