Question

look at this diagram: if $overleftrightarrow{oq}$ and $overleftrightarrow{rt}$ are parallel lines and $mangle rsp = 55^{circ}$, what is $mangle qps$?

Explanation:

Step1: Identify angle - relationship

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

Step2: Use the supplementary - angle property

The sum of supplementary angles is $180^{\circ}$. So, $m\angle RSP + m\angle QPS=180^{\circ}$.

Step3: Solve for $m\angle QPS$

Given $m\angle RSP = 55^{\circ}$, then $m\angle QPS=180^{\circ}-m\angle RSP$. Substitute $m\angle RSP = 55^{\circ}$ into the equation: $m\angle QPS = 180 - 55=125^{\circ}$.

Answer:

$125$