Question

look at this diagram: if $overleftrightarrow{oq}$ and $overleftrightarrow{rt}$ are parallel lines and $mangle rsp = 43^{circ}$, what is $mangle ops$?

Explanation:

Step1: Identify angle - relationship

$\angle RSP$ and $\angle OPS$ are supplementary angles since $\overleftrightarrow{OQ}$ and $\overleftrightarrow{RT}$ are parallel lines and $\overleftrightarrow{UN}$ is a transversal.

Step2: Use the supplementary - angle formula

The sum of supplementary angles is $180^{\circ}$. Let $m\angle RSP = 43^{\circ}$ and $m\angle OPS=x$. Then $x + 43^{\circ}=180^{\circ}$.

Step3: Solve for the unknown angle

$x=180^{\circ}- 43^{\circ}=137^{\circ}$.

Answer:

$137$