Question

look at this diagram: if $overleftrightarrow{oq}$ and $overleftrightarrow{rt}$ are parallel lines and $mangle qps = 134^{circ}$, what is $mangle ops$?

Explanation:

Step1: Recall linear - pair property

Linear - pair angles are supplementary, meaning they add up to 180°. $\angle QPS$ and $\angle OPS$ form a linear pair.
Let $m\angle OPS = x$. We know that $m\angle QPS=134^{\circ}$ and $m\angle QPS + m\angle OPS=180^{\circ}$.

Step2: Solve for $m\angle OPS$

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

Answer:

$46$