Question

which angles are alternate exterior angles?
diagram with lines oq, rt, and nu intersecting at p and s
options:
∠qps and ∠tsu
∠ops and ∠tsu
∠rsu and ∠qpn
∠rsp and ∠ops

Explanation:

Step1: Recall Alternate Exterior Angles Definition

Alternate exterior angles are formed when a transversal crosses two parallel lines. They lie outside the two lines and on opposite sides of the transversal.

Step2: Analyze Each Option

• Option 1: ∠QPS and ∠TSU

∠QPS is inside the two lines (PQ and RT), so not exterior. Eliminate.

• Option 2: ∠OPS and ∠TSU

∠OPS is outside PQ (left of PQ), ∠TSU is outside RT (right of RT), on opposite sides of transversal NU. Check if they are exterior: yes, both outside the parallel lines PQ and RT.

• Option 3: ∠RSU and ∠QPN

∠RSU is at S (below RT), ∠QPN is at P (above PQ). Their positions don’t match alternate exterior (should be on opposite sides of transversal, outside the two lines). Eliminate.

• Option 4: ∠RSP and ∠OPS

∠RSP is inside RT (left of S), ∠OPS is outside PQ (left of P). Not alternate exterior. Eliminate.

Answer:

∠OPS and ∠TSU (the second option: ∠OPS and ∠TSU)