Question

look at this diagram: if (overleftrightarrow{oq}) and (overleftrightarrow{rt}) are parallel lines and (mangle rsp = 68^{circ}), what is (mangle opn?)

Explanation:

Step1: Identify vertical angles

$\angle RSP$ and $\angle USP$ are supplementary (linear pair), but wait—$\angle RSP$ and $\angle OPN$: since $OQ \parallel RT$, transversal $UN$ creates corresponding angles. $\angle RSP$ and $\angle OPN$ are corresponding angles.

Step2: Corresponding angles property

Corresponding angles are equal when lines are parallel. So $m\angle OPN = m\angle RSP$.

Answer:

68