Question

which angles are corresponding angles? ∠qpn and ∠qps ∠qpn and ∠rsu ∠qpn and ∠tsp ∠qpn and ∠ops

Explanation:

Step1: Recall Corresponding Angles Definition

Corresponding angles are equal when two parallel lines are cut by a transversal. They occupy the same relative position at each intersection.

Step2: Analyze Each Option

• Option 1: $\angle QPN$ and $\angle QPS$: These are adjacent angles, not corresponding.
• Option 2: $\angle QPN$ and $\angle RSU$: When transversal $NU$ cuts parallel lines $OQ$ and $RT$, $\angle QPN$ (at $P$ on $OQ$) and $\angle RSU$ (at $S$ on $RT$) are in corresponding positions (both above the parallel lines, same side of transversal).
• Option 3: $\angle QPN$ and $\angle TSP$: $\angle TSP$ is below $RT$, not corresponding to $\angle QPN$ (above $OQ$).
• Option 4: $\angle QPN$ and $\angle OPS$: These are vertical or adjacent - not corresponding.

Answer:

$\angle QPN$ and $\angle RSU$ (the option with $\angle QPN$ and $\angle RSU$)