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: Identify supplementary angles

∠N + ∠O = 180° (NO transversal), ∠O + ∠P = 180° (OP transversal).

Step2: Apply supplements of same angle

∠N and ∠P are supplements of ∠O, so ∠N ≅ ∠P.

Answer:

∠N ≅ ∠P