Question

which angles are alternate exterior angles?
image of two parallel lines cut by a transversal, with points p, q, r on the top line; s, t, u on the bottom line; and o, q, t, v on the transversal
options:
∠pqt and ∠rqo
∠stq and ∠utv
∠utq and ∠stv
∠pqo and ∠utv

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: \( \angle PQT \) and \( \angle RQO \) – These are adjacent angles, not alternate exterior.
• Option 2: \( \angle STQ \) and \( \angle UTV \) – These are vertical angles or adjacent, not alternate exterior.
• Option 3: \( \angle UTQ \) and \( \angle STV \) – These are vertical angles, not alternate exterior.
• Option 4: \( \angle PQO \) and \( \angle UTV \) – \( \angle PQO \) is outside line \( PR \) (left side of transversal \( OV \)), \( \angle UTV \) is outside line \( SU \) (right side of transversal \( OV \)), and they are on opposite sides of transversal. So they are alternate exterior angles.

Answer:

\( \angle PQO \) and \( \angle UTV \) (the last option: \( \angle PQO \) and \( \angle UTV \))