Question

A partial proof was constructed given that MNOP is a parallelogram.

Answer 1

Answer:

D. ∠M ≅ ∠O; ∠N ≅ ∠P

Step-by-step explanation:

MNOP is a parallelogram with <M supplementary to <N, <P supplementary to <M and  <N supplementary to <O. We can therefore deduce that <O is supplementary to <P if OP will act as the transversal to MP and NO also, <O-=<M

Answer 2

A diagram of parallelogram MNOP is attached below

We have side MN || side OP and side MP || NO

Using the rule of angles in parallel lines, ∠M and ∠P are supplementary as well as ∠M and ∠N.

Since ∠M+∠P = 180° and ∠M+∠N=180°, we can conclude that ∠P and ∠N are of equal size. 

∠N and ∠O are supplementary by the rules of angles in parallel lines
∠O and ∠P are supplementary by the rules of angles in parallel lines

∠N+∠O=180° and ∠O+∠P=180°

∠N and ∠P are of equal size

we deduce further that ∠M and ∠O are of equal size

Hence, the correct statement to complete the proof is

∠M ≅ ∠O; ∠N ≅ ∠P