Question

oq and rt are parallel lines. select all the pairs of corresponding angles. ∠qps and ∠tsu ∠rsp and ∠qpn ∠tsu and ∠rsu ∠rsu and ∠tsp

Explanation:

Step1: Recall the definition of corresponding angles

Corresponding angles are angles that are in the same relative position with respect to the parallel lines and the transversal.

Step2: Analyze \(\angle QPS\) and \(\angle TSU\)

Since \(\overrightarrow{OQ}\parallel\overrightarrow{RT}\) and \(UN\) is a transversal. \(\angle QPS\) and \(\angle TSU\) are in the same relative position (above the parallel lines and on the same side of the transversal), so they are corresponding angles.

Step3: Analyze \(\angle RSP\) and \(\angle QPN\)

\(\overrightarrow{OQ}\parallel\overrightarrow{RT}\) and \(UN\) is a transversal. \(\angle RSP\) and \(\angle QPN\) are in the same relative position (below the parallel lines and on the same side of the transversal), so they are corresponding angles.

Step4: Analyze \(\angle TSU\) and \(\angle RSU\)

These two angles are adjacent angles (they share a common side \(SU\)) and not in the same relative position with respect to the parallel lines and a transversal, so they are not corresponding angles.

Step5: Analyze \(\angle RSU\) and \(\angle TSP\)

\(\overrightarrow{OQ}\parallel\overrightarrow{RT}\) and \(UN\) is a transversal. \(\angle RSU\) and \(\angle TSP\) are in the same relative position (below - left of the parallel lines and on the same side of the transversal), so they are corresponding angles.

Answer:

\(\angle QPS\) and \(\angle TSU\), \(\angle RSP\) and \(\angle QPN\), \(\angle RSU\) and \(\angle TSP\)