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, __________ and _________ because they are supplements of the same angle. Which statements should fill in the blanks in the last line of the proof?

∠M is supplementary to ∠N; ∠M is supplementary to ∠O
∠M is supplementary to ∠O; ∠N is supplementary to ∠P
∠M ≅ ∠P; ∠N ≅ ∠O
∠M ≅ ∠O; ∠N ≅ ∠P

Answer 1

Answer:∠M ≅ ∠O; ∠N ≅ ∠P

Explanation:

Already did it

Answer 2

∠M ≅ ∠O; ∠N ≅ ∠P

Explanation:

According to the problem

`\angle N + \angle O =180\°`

`\angle O + \angle P = 180\°`

`\angle M + \angle P = 180\°`

Which means,

`\angle N + \angle O = \angle O + \angle P\\\angle N = \angle P`

And,

`\angle O + \angle P = \angle M + \angle P\\\angle O = \angle M`

Therefore, the right answer is the last choice.