Question

in the diagram, the parallel lines m and n are cut by the transversal line t. which angles are congruent? a. ∠1 and ∠8 b. ∠2 and ∠8 c. ∠4 and ∠6 d. ∠4 and ∠7

Explanation:

Step1: Recall congruent angle rules

When parallel lines are cut by a transversal, alternate exterior angles are congruent.

Step2: Identify angle positions

∠2 is on the exterior of line m, ∠8 is on the exterior of line n, and they are on opposite sides of transversal t—so they are alternate exterior angles.

Step3: Verify congruence

Alternate exterior angles formed by parallel lines and a transversal are congruent, so ∠2 ≅ ∠8.

Answer:

B. ∠2 and ∠8