su and vx are parallel lines.

image of two vertical parallel lines (su and vx) and a transversal line (yr) intersecting them, with points labeled v, s, r, t, w, y, x, u

which angles are alternate exterior angles?

∠str and ∠vwy ∠str and ∠xwy
∠str and ∠stw ∠str and ∠utw

Question

su and vx are parallel lines.

image of two vertical parallel lines (su and vx) and a transversal line (yr) intersecting them, with points labeled v, s, r, t, w, y, x, u

which angles are alternate exterior angles?

∠str and ∠vwy    ∠str and ∠xwy
∠str and ∠stw    ∠str and ∠utw

Accepted Answer

# Brief Explanations:
To determine alternate exterior angles, we recall the definition: alternate exterior angles are formed when a transversal crosses two parallel lines, lying outside the two parallel lines and on opposite sides of the transversal.
- For $\angle STR$ and $\angle VWY$: $\angle STR$ is at the intersection of transversal $YR$ and $SU$, $\angle VWY$ is at the intersection of $YR$ and $VX$. $SU$ and $VX$ are parallel. $\angle STR$ is outside? No, $\angle STR$ is between $SU$ and $YR$ (interior? Wait, no—wait, $SU$ and $VX$ are vertical parallel lines. The transversal is $YR$. Exterior angles are outside the two parallel lines (the region not between $SU$ and $VX$).
- $\angle STR$: Let's visualize. $SU$ and $VX$ are parallel (vertical). Transversal $YR$ crosses them. $\angle STR$ is at $T$ (on $SU$), $\angle XWY$ is at $W$ (on $VX$). Wait, no—let's check positions.
Wait, correct approach: Alternate exterior angles are outside the two parallel lines (so not between $SU$ and $VX$) and on opposite sides of the transversal.
- $\angle STR$ and $\angle XWY$: Wait, no. Wait, $\angle STR$ is above $SU$ (since $SU$ is vertical, $T$ is on $SU$, $R$ is going up-right). $\angle XWY$ is at $W$ on $VX$, $Y$ is going down-left. Wait, maybe I got the lines wrong. $SU$ and $VX$ are parallel (both vertical, upward and downward arrows). Transversal is $YR$ (from $Y$ down-left to $R$ up-right).
So the two parallel lines are $SU$ (through $S, T, U$) and $VX$ (through $V, W, X$). The transversal is $YR$ (through $Y, W, T, R$).
Exterior regions: outside the area between $SU$ and $VX$. So for $SU$, the exterior is above $S$ or below $U$; for $VX$, above $V$ or below $X$.
$\angle STR$: at $T$, between $SU$ and $YR$? No, $SU$ is vertical, $YR$ is slanting. Wait, $\angle STR$ is formed by $ST$ (vertical) and $TR$ (slanting). So $\angle STR$ is on the "outside" of $VX$ (since $VX$ is to the left of $SU$)? Wait, maybe better to use the definition: alternate exterior angles are non - adjacent, outside the two parallel lines, and on opposite sides of the transversal.
Let's check each option:
1. $\angle STR$ and $\angle VWY$: $\angle VWY$ is at $W$, between $VX$ and $YR$ (interior?), no.
2. $\angle STR$ and $\angle XWY$: $\angle XWY$ is at $W$, below $VX$ (exterior of $VX$ - $SU$ region), and $\angle STR$ is above $SU$ (exterior of $VX$ - $SU$ region), on opposite sides of transversal $YR$. Wait, no—wait, $\angle STR$ is at $T$ (on $SU$), $\angle XWY$ is at $W$ (on $VX$). Are they outside the two parallel lines? The two parallel lines are $SU$ and $VX$. The area between them is between the two vertical lines. So $\angle STR$ is to the right of $SU$ (outside the region between $SU$ and $VX$), and $\angle XWY$ is to the left of $VX$ (outside the region between $SU$ and $VX$)? No, that's not right. Wait, maybe I mixed up.
Wait, let's re - define: When two parallel lines are cut by a transversal, alternate exterior angles are:
- Outside the two parallel lines (i.e., not between the two lines)
- On opposite sides of the transversal.

So for lines $SU$ (vertical, from $S$ down to $U$) and $VX$ (vertical, from $V$ down to $X$), the region between them is the space between these two vertical lines. Exterior is outside this space. The transversal is $YR$ (from $Y$ (down - left) to $R$ (up - right)).

$\angle STR$: at point $T$ (on $SU$), formed by $ST$ (up along $SU$) and $TR$ (up - right along $YR$). So this angle is to the right of $SU$ (outside the region between $SU$ and $VX$, since $VX$ is to the left of $SU$).

$\angle XWY$: at point $W$ (on $VX$), formed by $XW$ (down along $VX$) and $WY$ (down - left along $YR$). This angle is to the left of $VX$ (outside the region between $SU$ and $VX$). Wait, no—maybe I have the direction wrong. Let's look at the other options.

Wait, $\angle STR$ and $\angle XWY$: Wait, no, let's check the other options. $\angle STR$ and $\angle VWY$: $\angle VWY$ is at $W$, above $VX$ (between $VX$ and $SU$? No, $VX$ and $SU$ are parallel vertical. $\angle VWY$ is at $W$, between $VX$ and $YR$? No.

Wait, maybe the correct pair is $\angle STR$ and $\angle XWY$? Wait, no—wait, let's recall: alternate exterior angles are equal and outside the two parallel lines. Let's take the two parallel lines as $l_1 = SU$ and $l_2 = VX$, transversal $t = YR$.

For $\angle STR$ (at $T$ on $l_1$) and $\angle XWY$ (at $W$ on $l_2$):
- $\angle STR$ is outside $l_1$ and $l_2$ (since it's to the right of $l_1$, and $l_2$ is to the left of $l_1$, so the area between $l_1$ and $l_2$ is to the left of $l_1$ and right of $l_2$; $\angle STR$ is to the right of $l_1$, so outside the between - region).
- $\angle XWY$ is outside $l_1$ and $l_2$ (to the left of $l_2$, so outside the between - region).
- They are on opposite sides of the transversal $t$ ( $\angle STR$ is on the right side of $t$ (since $t$ is $YR$, going from $Y$ (left - down) to $R$ (right - up); so the right side of $t$ is where $R$ is, left side is where $Y$ is). $\angle STR$ is on the right side of $t$ (at $T$, $R$ is up - right from $T$), $\angle XWY$ is on the left side of $t$ (at $W$, $Y$ is down - left from $W$).

Now check other options:
- $\angle STR$ and $\angle STW$: These are adjacent or same - side, not alternate exterior.
- $\angle STR$ and $\angle UTW$: These are adjacent or related to the same line, not alternate exterior.
- $\angle STR$ and $\angle VWY$: $\angle VWY$ is between $VX$ and $YR$ (interior region), so not exterior.

So the correct pair is $\angle STR$ and $\angle XWY$.
# Answer: $\angle STR$ and $\angle XWY$

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