Question

1. which conclusion can you make from the given statements? if a transversal crosses parallel lines then alternate exterior angles are congruent. line l 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:

Step1: Recall alternate - exterior angles definition

Alternate - exterior angles are non - adjacent angles that lie outside two parallel lines and on opposite sides of a transversal.

Step2: Identify alternate - exterior angles in the figure

In the given figure, when line \(l\) is a transversal to parallel lines \(m\) and \(n\), \(\angle1\) and \(\angle7\) are alternate - exterior angles.

Step3: Apply the property of alternate - exterior angles

Since if a transversal crosses parallel lines then alternate - exterior angles are congruent, and \(\angle1\) and \(\angle7\) are alternate - exterior angles, \(\angle1\cong\angle7\).

Answer:

A. \(\angle1\) is congruent to \(\angle7\)