the diagram shows isosceles trapezoid lmnp. it also shows how line segment no was drawn to form…

Explanation:

Step1: Recall parallelogram property

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

Step2: Use isosceles - trapezoid property

In isosceles trapezoid LMNP, $\angle L+\angle NLP = 180^{\circ}$ (adjacent angles along a non - parallel side are supplementary). Also, since LMNP is isosceles, $\angle L=\angle P = 50^{\circ}$. In $\triangle ONP$, we know that $\angle NOP=\angle L = 50^{\circ}$ (corresponding angles of parallel lines LM and NO). Since the sum of angles in a triangle is $180^{\circ}$, and in $\triangle ONP$, let $\angle ONP = x$. We know that $\angle NOP+\angle ONP+\angle OPN=180^{\circ}$. In isosceles trapezoid LMNP, $\angle OPN=\angle L = 50^{\circ}$. So, $x + 50^{\circ}+50^{\circ}=180^{\circ}$. $x=180^{\circ}-(50^{\circ}+50^{\circ})$. $x = 80^{\circ}$.

Answer:

$80^{\circ}$