Question

a partial proof was constructed given that mnop is a parallelogram. by the definition of a parallelogram, mn || po and mp || no. using mp as a transversal, ∠m and ∠p are same - side interior angles, so they are supplementary. using no as a transversal, ∠n and ∠o are same - side interior angles, so they are supplementary. using op as a transversal, ∠o and ∠p are same - side interior angles, so they are supplementary. therefore, ____________ because they are supplements of the same angle. which statement should fill in the blank in the last line of the proof? ∠m is supplementary to ∠o ∠n is supplementary to ∠p ∠m ≅ ∠p ∠n ≅ ∠p

Explanation:

Step1: Recall angle - properties of parallelogram

In parallelogram MNOP, we know that when two parallel lines are cut by a transversal, same - side interior angles are supplementary.

Step2: Analyze the given supplementary angle pairs

We have ∠M and ∠P are supplementary (using MP as transversal), ∠N and ∠O are supplementary (using NO as transversal), and ∠O and ∠P are supplementary (using OP as transversal).

Step3: Use the property of supplements of the same angle

If ∠M + ∠P=180° and ∠O + ∠P = 180°, then ∠M and ∠O are supplements of the same angle (∠P). So ∠M≅∠O. Similarly, if ∠N+∠O = 180° and ∠O + ∠P=180°, then ∠N≅∠P.

Answer:

∠N≅∠P