a partial proof was constructed given that mnop is a parallelogram. which statement should fill in the blank in the last line of the proof? by the definition of a parallelogram, $ \overline { m n } \parallel \overline { p o } $ and $ \overline { m p } \parallel \overline { n o } $. using $ \overline { m p } $ as a transversal, $ \angle m $ and $ \angle p $ are same - side interior angles, so they are supplementary. using $ \overline { n o } $ as a transversal, $ \angle n $ and $ \angle o $ are same - side interior angles, so they are supplementary. using $ \overline { o p } $ as a transversal, $ \angle o $ and $ \angle p $ are same - side interior angles, so they are supplementary. therefore, ______________ because they are supplements of the same angle. $ \angle m $ is supplementary to $ \angle o $ $ \angle n $ is supplementary to $ \angle p $ $ \angle m \cong \angle p $ $ \angle n \cong \angle p $

Question

Accepted Answer

# Brief Explanations:
We know that $\angle M+\angle P = 180^{\circ}$ (since they are same - side interior angles with transversal $MP$) and $\angle O+\angle P=180^{\circ}$ (since they are same - side interior angles with transversal $OP$). If $\angle M+\angle P=\angle O + \angle P$, then by the subtraction property of equality ($\angle M+\angle P-\angle P=\angle O+\angle P - \angle P$), we get $\angle M=\angle O$. Also, $\angle N+\angle O = 180^{\circ}$ (same - side interior angles with transversal $NO$) and $\angle O+\angle P=180^{\circ}$. If two angles are supplementary to the same angle, then they are congruent. So $\angle N$ and $\angle P$ are supplementary to $\angle O$ and $\angle O$ respectively (wait, no: $\angle N$ and $\angle O$ are same - side interior angles ($\angle N+\angle O = 180^{\circ}$), $\angle O$ and $\angle P$ are same - side interior angles ($\angle O+\angle P=180^{\circ}$). So $\angle N$ and $\angle P$ are supplements of the same angle ($\angle O$).

# Answer:
$\angle N\cong\angle P$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Answer: