Question

look at this diagram: if $overleftrightarrow{oq}$ and $overleftrightarrow{rt}$ are parallel lines and $mangle rsp = 138^{circ}$, what is $mangle qps?$

Explanation:

Step1: Identify angle - relationship

$\angle RSP$ and $\angle QPS$ are same - side interior angles.

Step2: Apply the property of parallel lines

For parallel lines $\overleftrightarrow{OQ}$ and $\overleftrightarrow{RT}$, same - side interior angles are supplementary, i.e., $m\angle RSP + m\angle QPS=180^{\circ}$.

Step3: Solve for $m\angle QPS$

$m\angle QPS = 180^{\circ}-m\angle RSP$. Given $m\angle RSP = 138^{\circ}$, then $m\angle QPS=180 - 138=42^{\circ}$.

Answer:

$42$