Question

in the accompanying diagram, lines a and b are parallel, and lines c and d are transversals. which angle is congruent to angle 8?

Explanation:

Step1: Recall parallel - line properties

When two parallel lines are cut by a transversal, corresponding angles are congruent, vertical angles are congruent, and alternate - interior and alternate - exterior angles are congruent. Angle 8 and angle 6 are vertical angles.

Step2: Use vertical - angle congruence

Vertical angles are always congruent. Since angle 8 and angle 6 are vertical angles formed by the intersection of line \(d\) with another line, \(\angle8\cong\angle6\). Also, since lines \(a\) and \(b\) are parallel and \(d\) is a transversal, \(\angle8\) and \(\angle2\) are alternate - exterior angles, so \(\angle8\cong\angle2\).

Answer:

Angle 2 and Angle 6