Question

look at this diagram: if $overleftrightarrow{ln}$ and $overleftrightarrow{oq}$ are parallel lines and $mangle qpr = 46^{circ}$, what is $mangle opr$?

Explanation:

Step1: Identify angle - relationship

$\angle QPR$ and $\angle OPR$ are supplementary angles since $\overrightarrow{OQ}$ is a straight - line.

Step2: Use the supplementary - angle formula

The sum of supplementary angles is $180^{\circ}$. Let $m\angle QPR = 46^{\circ}$ and $m\angle OPR=x$. Then $x + 46^{\circ}=180^{\circ}$.

Step3: Solve for the unknown angle

$x=180^{\circ}- 46^{\circ}=134^{\circ}$.

Answer:

$134$