Question

maria drew two parallel lines, kl and mn, intersected by a transversal pq, as shown below: which fact would help maria prove that the measure of angle krq is equal to the measure of angle msq? alternate interior angles krs and rsn are equal, and consecutive angles krs and krp are complementary alternate interior angles lrs and rsn are equal, and vertical angles rsn and msq are supplementary vertical angles msq and rsn are equal, and alternate interior angles krs and rsn are equal vertical angles lrs and krp are equal, and same - side, consecutive interior angles prl and lrs are equal

Explanation:

Step1: Recall angle - relationship properties

When two parallel lines are intersected by a transversal, we use the properties of vertical angles and alternate - interior angles.

Step2: Analyze vertical angles

Vertical angles are equal. Angle MSQ and angle RSN are vertical angles, so $\angle MSQ=\angle RSN$.

Step3: Analyze alternate - interior angles

Alternate - interior angles formed by two parallel lines and a transversal are equal. Since KL and MN are parallel and PQ is a transversal, $\angle KRS=\angle RSN$.

Step4: Use the transitive property

If $\angle MSQ = \angle RSN$ and $\angle KRS=\angle RSN$, then by the transitive property of equality, $\angle KRQ=\angle MSQ$.

Answer:

C. Vertical angles MSQ and RSN are equal, and alternate interior angles KRS and RSN are equal