Two parallel lines are cut by a transversal. What is true about the pair of alternate exterior angles?

Two parallel lines are cut by a transversal. What is true about the pair of alternate exterior angles?

• A. Congruent
• B. Supplementary
• C. Adjacent
• D. Vertical

Answer: (A)

When two parallel lines are cut by a transversal, alternate exterior angles are congruent. These angles lie outside the two lines and on opposite sides of the transversal, and the parallelism forces the angle the transversal makes with one line to match the angle it makes with the other. So, the two alternate exterior angles have equal measures. They’re not supplementary (that relation occurs for same-side interior angles), not adjacent (they don’t share a side), and not vertical (they aren’t formed by a single intersection). Therefore, the pair is congruent.

When two parallel lines are cut by a transversal, alternate exterior angles are congruent. These angles lie outside the two lines and on opposite sides of the transversal, and the parallelism forces the angle the transversal makes with one line to match the angle it makes with the other. So, the two alternate exterior angles have equal measures.

They’re not supplementary (that relation occurs for same-side interior angles), not adjacent (they don’t share a side), and not vertical (they aren’t formed by a single intersection). Therefore, the pair is congruent.