Question

the diagram shows isosceles trapezoid lmnp. it also shows how line segment no was drawn to form parallelogram lmno. what is the measure of angle onp? 50° 65° 80° 130°

Explanation:

Step1: Recall property of parallelogram

In parallelogram LMNO, opposite - angles are equal. So, $\angle L=\angle MNO = 50^{\circ}$.

Step2: Recall property of isosceles trapezoid

In isosceles trapezoid LMNP, $\angle L+\angle MNP = 180^{\circ}$ (adjacent - angles along non - parallel sides are supplementary). Let $\angle ONP=x$. Then $\angle MNO + x=\angle MNP$. Since $\angle L = 50^{\circ}$, $\angle MNP=180^{\circ}-\angle L = 130^{\circ}$.

Step3: Calculate $\angle ONP$

We know that $\angle MNO = 50^{\circ}$ and $\angle MNP = 130^{\circ}$. So, $x=\angle ONP=\angle MNP-\angle MNO$. Substituting the values, we get $\angle ONP = 130^{\circ}-50^{\circ}=80^{\circ}$.

Answer:

$80^{\circ}$