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 b. ∠7 ∠1 is congruent to ∠5 c. ∠4 is congruent to ∠8 d. ∠4 is congruent to ∠6

Explanation:

Step1: Recall alternate - exterior angles property

When a transversal crosses parallel lines, alternate - exterior angles are congruent. In the given figure, for parallel lines \(m\) and \(n\) with transversal \(t\), \(\angle4\) and \(\angle8\) are alternate - exterior angles.

Step2: Analyze each option

• Option A: \(\angle1\) and \(\angle7\) are not related by the alternate - exterior angles property.
• Option B: \(\angle1\) and \(\angle5\) are corresponding angles, not alternate - exterior angles.
• Option C: Since \(\angle4\) and \(\angle8\) are alternate - exterior angles for parallel lines \(m\) and \(n\) cut by transversal \(t\), \(\angle4\cong\angle8\) according to the property of parallel lines and transversals.
• Option D: \(\angle4\) and \(\angle6\) are not alternate - exterior angles.

Answer:

C. \(\angle4\) is congruent to \(\angle8\)