Question

oq and rt are parallel lines. which angles are alternate exterior angles? ∠qpn and ∠rsp ∠qpn and ∠tsp ∠qpn and ∠rsu ∠qpn and ∠opn

Explanation:

Step1: Recall the definition of alternate exterior angles

Alternate exterior angles are non - adjacent exterior angles that lie on opposite sides of the transversal.

Step2: Analyze each option

• For \(\angle QPN\) and \(\angle RSP\):
• \(\angle QPN\) is an exterior angle. \(\angle RSP\) is an interior angle. So they are not alternate exterior angles.
• For \(\angle QPN\) and \(\angle TSP\):
• \(\angle QPN\) and \(\angle TSP\) are non - adjacent and lie on opposite sides of the transversal \(NU\). \(\angle QPN\) is an exterior angle (outside the region between \(OQ\) and \(RT\)) and \(\angle TSP\) is also an exterior angle.
• For \(\angle QPN\) and \(\angle RSU\):
• \(\angle RSU\) and \(\angle QPN\) are not in the correct position (not non - adjacent exterior angles on opposite sides of the transversal in the sense of alternate exterior angles).
• For \(\angle QPN\) and \(\angle OPN\):
• \(\angle QPN\) and \(\angle OPN\) are adjacent angles (they share a common side \(PN\)). So they are not alternate exterior angles.

Answer:

\(\angle QPN\) and \(\angle TSP\)