Question

which conclusion can you make from the given statements? if a transversal crosses parallel lines, then alternate exterior angles are congruent. line t crosses parallel lines m and n. a. ∠1 is congruent to ∠7 b. ∠1 is congruent to ∠5 c. ∠4 is congruent to ∠8 d. ∠4 is congruent to ∠6

Explanation:

1. Recall the definition of alternate exterior angles: When a transversal crosses two parallel lines, alternate exterior angles are on opposite sides of the transversal and outside the two parallel lines.
2. Analyze each option:

• Option A: ∠1 and ∠7. ∠1 is outside line m, ∠7 is outside line n, and they are on opposite sides of transversal t. So they are alternate exterior angles. By the given statement, alternate exterior angles are congruent, so ∠1 ≅ ∠7.
• Option B: ∠1 and ∠5 are corresponding angles (not alternate exterior), so this is incorrect.
• Option C: ∠4 and ∠8. ∠4 is inside line m, ∠8 is outside line n, so they are not alternate exterior angles. Incorrect.
• Option D: ∠4 and ∠6 are alternate interior angles, not exterior. Incorrect.

Answer:

A. ∠1 is congruent to ∠7