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 properties of parallelogram

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

Step2: Recall properties of isosceles trapezoid

In isosceles trapezoid LMNP, $\angle L+\angle MPN = 180^{\circ}$ (adjacent - base angles along a non - parallel side are supplementary). Also, since LMNP is isosceles, $\angle MPN=\angle LNP$.

Step3: Calculate $\angle LNP$

$\angle LNP = 180^{\circ}-\angle L=180 - 50=130^{\circ}$.

Step4: Find $\angle ONP$

$\angle ONP=\angle LNP-\angle MNO$. Substitute $\angle LNP = 130^{\circ}$ and $\angle MNO = 50^{\circ}$. So, $\angle ONP=130 - 50=80^{\circ}$.

Answer:

$80^{\circ}$