Question

which angles are alternate exterior angles?
∠onl and ∠mnq , ∠mnl and ∠rqs
∠pqn and ∠onl ∠rqs and ∠mnq

Explanation:

Step1: Recall Alternate Exterior Angles Definition

Alternate exterior angles are formed when a transversal crosses two parallel lines (or lines that appear parallel here). They lie outside the two lines and on opposite sides of the transversal.

Step2: Analyze Each Option

• Option 1: \( \angle ONL \) and \( \angle MNQ \) – These are not exterior (or their positions don't fit alternate exterior).
• Option 2: \( \angle MNL \) and \( \angle RQS \) – Check positions: \( \angle MNL \) and \( \angle RQS \) are outside the two vertical lines (PQ and MO) and on opposite sides of transversal SL. Wait, no, re - check. Wait, the two lines are PQ (with points P, Q, R) and MO (with points M, N, O). Transversal is SL (with points S, Q, N, L).
• Option 3: \( \angle PQN \) and \( \angle ONL \) – Positions don't fit alternate exterior.
• Option 4: \( \angle RQS \) and \( \angle MNQ \) – Positions don't fit. Wait, re - evaluating. Wait, \( \angle RQS \) is at Q, outside the two lines (PQ and MO), on one side of transversal. \( \angle MNL \): Wait, maybe I made a mistake. Wait, the correct alternate exterior angles should be \( \angle RQS \) and \( \angle MNL \)? No, the option is \( \angle MNL \) and \( \angle RQS \). Wait, let's re - define: two lines cut by transversal. Exterior angles are outside the two lines. Alternate means opposite sides of transversal. So for lines PQ and MO, transversal SL. \( \angle RQS \) is at Q (below PQ, left of transversal), \( \angle MNL \) is at N (above MO, right of transversal). Wait, no, maybe the correct pair is \( \angle RQS \) and \( \angle MNL \)? But the option is \( \angle MNL \) and \( \angle RQS \). Wait, among the options, \( \angle MNL \) and \( \angle RQS \) are alternate exterior angles. Let's check again. The two lines are PQ (vertical) and MO (vertical). Transversal is SL (diagonal). \( \angle RQS \) is outside the two lines (below PQ, left of transversal), \( \angle MNL \) is outside the two lines (above MO, right of transversal). They are on opposite sides of the transversal and outside the two lines. So they are alternate exterior angles.

Answer:

\( \angle MNL \) and \( \angle RQS \) (the option with \( \angle MNL \) and \( \angle RQS \))