Chapter 9.1, Problem 73E

The sketch shows parallel lines m and n cut by a transversal q. Complete the steps to prove that alternate exterior angles have the same measure.

(a) Measure of $\measuredangle 2=$ measure of $\measuredangle$ ____ since they are vertical angles.

(b) Measure of $\measuredangle 3=$ measure of $\measuredangle$ ____ since they are alternate interior angles.

(c) Measure of $\measuredangle 6=$ measure of $\measuredangle$ ____ since they are vertical angles.

(d) By the results of parts (a), (b), and (c), the measure of $\measuredangle 2$ must equal the measure of $\measuredangle$ ____, showing that alternate ____ angles have equal measures.