Question

which angles are alternate exterior angles?
image of intersecting lines with points w, t, z, x, u, s, y, v
∠tux and ∠yxu
∠tus and ∠yxz
∠wxz and ∠wxu
∠tux and ∠wxu

Explanation:

Step1: Recall Alternate Exterior Angles Definition

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

Step2: Analyze Each Option

• Option 1: \( \angle TUX \) and \( \angle YXU \) – These are interior angles (between the two lines), not exterior.
• Option 2: \( \angle TUS \) and \( \angle YXZ \) – \( \angle TUS \) is outside the two lines (exterior) and \( \angle YXZ \) is also outside the two lines, on opposite sides of the transversal. Check their positions: transversal is \( ZS \), lines are \( WY \) and \( TV \). \( \angle TUS \) is at \( U \) (exterior, above \( TV \), right of transversal), \( \angle YXZ \) is at \( X \) (exterior, above \( WY \), left of transversal). So they fit alternate exterior.
• Option 3: \( \angle WXZ \) and \( \angle WXU \) – These are adjacent angles, not alternate exterior.
• Option 4: \( \angle TUX \) and \( \angle WXU \) – These are interior angles (between the lines), not exterior.

Answer:

\( \angle TUS \) and \( \angle YXZ \)