Question

which angles are alternate exterior angles?
∠wxz and ∠yxu ∠tus and ∠vux
∠vus and ∠yxz ∠yxz and ∠tus

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

- For \( \angle WXZ \) and \( \angle YXU \): These are vertical angles (opposite angles formed by intersecting lines), not alternate exterior.
- For \( \angle TUS \) and \( \angle VUX \): These are adjacent angles or vertical? Wait, no, \( \angle TUS \) and \( \angle VUX \) – actually, let's check the lines. The two parallel lines are \( TV \) and \( WY \), transversal is \( SZ \).
- For \( \angle VUS \) and \( \angle YXZ \): Wait, no, let's re - examine. The correct pair: \( \angle VUS \) (exterior to \( TV \) and \( WY \), on one side of transversal) and \( \angle YXZ \) (exterior to \( TV \) and \( WY \), on the other side of transversal). Wait, actually, the correct pair is \( \angle VUS \) and \( \angle YXZ \)? Wait, no, let's look again. Wait, the two parallel lines are \( TV \) (with points \( T, U, V \)) and \( WY \) (with points \( W, X, Y \)). Transversal is \( SZ \) (with points \( S, U, X, Z \)).
Alternate exterior angles: lie outside the two parallel lines, on opposite sides of the transversal.
\( \angle VUS \): outside \( TV \) and \( WY \), above the transversal? Wait, no, \( TV \) and \( WY \) are the two parallel lines (horizontal? Wait, the arrows: \( TV \) is going left - right ( \( T \) left, \( V \) right), \( WY \) is also left - right ( \( W \) left, \( Y \) right). Transversal \( SZ \) is going up - down ( \( S \) up, \( Z \) down).
So exterior angles: for \( TV \) and \( WY \), the exterior regions are above \( TV \) and below \( WY \), or below \( TV \) and above \( WY \)? Wait, no, alternate exterior angles are on opposite sides of the transversal and outside the two lines.
So \( \angle VUS \): is at \( U \), above \( TV \), outside the two lines (since \( TV \) and \( WY \) are between the two parts of the transversal? Wait, maybe I made a mistake. Let's check the options again.
Wait the options:
1. \( \angle WXZ \) and \( \angle YXU \): these are vertical angles (opposite angles at \( X \)), so not alternate exterior.
2. \( \angle TUS \) and \( \angle VUX \): these are adjacent or vertical? \( \angle TUS \) and \( \angle VUX \) – \( \angle TUS \) is at \( U \), between \( T \) and \( S \), \( \angle VUX \) is at \( U \), between \( V \) and \( X \)? No, they are vertical angles? No, maybe not.
3. \( \angle VUS \) and \( \angle YXZ \): \( \angle VUS \) is at \( U \), outside the two lines ( \( TV \) and \( WY \)) on one side of transversal \( SZ \), \( \angle YXZ \) is at \( X \), outside the two lines on the other side of transversal \( SZ \). So they are alternate exterior angles.
Wait, but let's confirm the definition: Alternate exterior angles are two angles that lie outside the two lines cut by a transversal, and on opposite sides of the transversal.
So for lines \( TV \) (line 1) and \( WY \) (line 2), cut by transversal \( SZ \):
- \( \angle VUS \): outside line 1 ( \( TV \)) and line 2 ( \( WY \)), on the right - side of transversal \( SZ \).
- \( \angle YXZ \): outside line 1 ( \( TV \)) and line 2 ( \( WY \)), on the left - side of transversal \( SZ \).
So they are alternate exterior angles. Wait, but maybe I misread the options. Wait the last option is \( \angle YXZ \) and \( \angle TUS \)? Wait no, the options are:
\( \angle WXZ \) and \( \angle YXU \); \( \angle TUS \) and \( \angle VUX \); \( \angle VUS \) and \( \angle YXZ \); \( \angle YXZ \) and \( \angle TUS \)? Wait maybe a typo, but assuming the third option is \( \angle VUS \) and \( \angle YXZ \), that's the correct pair. Wait, but let's check again.
Wait, the two parallel lines are \( TV \) and \( WY \), transversal \( SZ \).
Alternate exterior angles:
- Above \( TV \) and below \( WY \), on opposite sides of transversal.
\( \angle VUS \) is above \( TV \), on the right of \( SZ \).
\( \angle YXZ \) is below \( WY \), on the left of \( SZ \).
Yes, so they are alternate exterior angles. The other options:
- \( \angle WXZ \) and \( \angle YXU \): vertical angles (opposite angles at \( X \)), so not alternate exterior.
- \( \angle TUS \) and \( \angle VUX \): these are vertical angles (opposite angles at \( U \)), so not alternate exterior.
- The last option (if it's \( \angle YXZ \) and \( \angle TUS \)): no, \( \angle TUS \) is adjacent or something else.
So the correct pair is \( \angle VUS \) and \( \angle YXZ \) (the third option? Wait the options as given: " \( \angle VUS \) and \( \angle YXZ \)" is one of the options? Wait the user's options:
" \( \angle WXZ \) and \( \angle YXU \)
\( \angle TUS \) and \( \angle VUX \)
\( \angle VUS \) and \( \angle YXZ \)
\( \angle YXZ \) and \( \angle TUS \)"
Wait, maybe a formatting error, but the correct alternate exterior angles are \( \angle VUS \) and \( \angle YXZ \).

Answer:

\( \angle VUS \) and \( \angle YXZ \)