Question

look at this diagram: if $overleftrightarrow{oq}$ and $overleftrightarrow{rt}$ are parallel lines and $mangle rsp = 54^{circ}$, what is $mangle qps$?

Explanation:

Step1: Identify angle - relationship

$\angle RSP$ and $\angle QPS$ are alternate - interior angles.

Step2: Apply property of alternate - interior angles

For parallel lines $\overleftrightarrow{OQ}$ and $\overleftrightarrow{RT}$ cut by a transversal, alternate - interior angles are congruent. So $m\angle QPS=m\angle RSP$.

Answer:

$54$