Question

\overleftrightarrow{oq} and \overleftrightarrow{rt} are parallel lines.

which angles are alternate interior angles?

\angle qpn and \angle ops
\angle tsu and \angle qps
\angle rsu and \angle tsu
\angle ops and \angle tsn

Explanation:

Step1: Recall the definition of alternate interior angles

Alternate interior angles are formed when a transversal crosses two parallel lines. They lie between the two parallel lines and on opposite sides of the transversal.

Step2: Analyze each option

• For $\angle QPN$ and $\angle OPS$: These are vertical angles (opposite angles formed by two intersecting lines), not alternate interior angles.
• For $\angle TSU$ and $\angle QPS$: $\overleftrightarrow{OQ}\parallel\overleftrightarrow{RT}$, and the transversal is $\overleftrightarrow{UN}$. $\angle TSU$ and $\angle QPS$ lie between the parallel lines $\overleftrightarrow{OQ}$ and $\overleftrightarrow{RT}$ and on opposite sides of the transversal $\overleftrightarrow{UN}$.
• For $\angle RSU$ and $\angle TSU$: These are adjacent angles (share a common side and vertex), not alternate interior angles.
• For $\angle OPS$ and $\angle TSR$ (assuming the last option was a typo and should be $\angle TSR$ or similar): Incorrect as per the position relative to the parallel lines and transversal.

Answer:

$\angle TSU$ and $\angle QPS$