Question

look at this diagram: if $overleftrightarrow{oq}$ and $overleftrightarrow{rt}$ are parallel lines and $mangle qps = 51^{circ}$, what is $mangle rsp$?

Explanation:

Step1: Recall angle - relationship

$\angle QPS$ and $\angle RSP$ 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 $m\angle QPS = 51^{\circ}$ and $m\angle RSP=x$. Then $x + 51^{\circ}=180^{\circ}$.

Step3: Solve for the unknown angle

$x=180^{\circ}- 51^{\circ}=129^{\circ}$.

Answer:

$129$