Question

oq and rt are parallel lines. select all the pairs of alternate interior angles. ∠qps and ∠opn ∠rsu and ∠rsp ∠rsp and ∠qps ∠rsu and ∠qps

Explanation:

Step1: Recall the definition of alternate interior angles

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

Step2: Analyze each pair

• For \(\angle QPS\) and \(\angle OPN\):
• \(\overrightarrow{OQ}\) and \(\overrightarrow{RT}\) are parallel. The transversal is \(\overrightarrow{NU}\). \(\angle QPS\) and \(\angle OPN\) are vertical angles (not alternate interior angles).
• For \(\angle RSU\) and \(\angle RSP\):
• These angles are adjacent angles (not alternate interior angles).
• For \(\angle RSP\) and \(\angle QPS\):
• Since \(\overrightarrow{OQ}\parallel\overrightarrow{RT}\) and \(\overrightarrow{NU}\) is the transversal. \(\angle RSP\) and \(\angle QPS\) lie between the parallel lines \(\overrightarrow{OQ}\) and \(\overrightarrow{RT}\) and on opposite sides of the transversal \(\overrightarrow{NU}\), so they are alternate interior angles.
• For \(\angle RSU\) and \(\angle QPS\):
• \(\angle RSU\) and \(\angle QPS\) are not alternate interior angles.

Answer:

\(\angle RSP\) and \(\angle QPS\)