Question

Estelle drew two parallel lines PQ and R0S intersected by a transversal KL, as shown below: Which theorem could Estelle use to show the measure of angle KMQ is equal to the measure of angle RNL?

Answer 1

Angle KMQ and angle RNL are  on apposite sides of the transversal and between above and below (exterior to) the parallel lines, so they are alternate exterior angles.  Theorem - Alternate exterior angles formed by parallel lines and a transversal have the same measure.

Answer 2

Answer: Alternative exterior angle theorem.

Explanation:

Since, here PQ and RS are parallel lines and these lines are cut by the same transversal  KL.

And, According to the Alternative exterior angle theorem, when two parallel lines are cut by a transversal , the resulting alternate exterior angles made by these parallel lines are congruent.

After making the diagram of the above situation, we found that $\angle KMQ$ ( on line PQ) and $\angle RNL$(on line RS)  are alternative angles made by common transversal KL.

Thus, according to the above theorem they must be equal to each other.

That is, $m\angle KMQ=m\angle RNL$.