Question

which angles are consecutive interior angles?
∠tux and ∠wxu
∠tus and ∠yxz
∠tus and ∠wxz
∠wxu and ∠yxz

Explanation:

Step1: Recall Consecutive Interior Angles

Consecutive interior angles are formed when a transversal crosses two parallel lines (or lines that appear parallel here). They lie between the two lines and on the same side of the transversal.

Step2: Analyze Each Option

• Option 1: $\angle TUX$ and $\angle WXU$: Check their positions. The transversal is $ZS$, and the two lines are $WY$ and $TV$. $\angle TUX$ and $\angle WXU$ are between the two lines (interior) and on the same side of transversal $ZS$? Wait, no, let's re - check. Wait, actually, for consecutive interior angles, they should be between the two lines cut by the transversal and on the same side of the transversal. Let's look at the lines: $WY$ and $TV$ are the two lines, $ZS$ is the transversal. $\angle WXU$ is at $X$ (on $WY$ and $ZS$), $\angle TUX$ is at $U$ (on $TV$ and $ZS$). Wait, maybe I made a mistake. Wait, another approach: Consecutive interior angles are supplementary when lines are parallel. But let's check the positions. The correct pair should be $\angle TUX$ and $\angle WXU$? Wait, no, let's check the other options.
• Option 2: $\angle TUS$ and $\angle YXZ$: $\angle TUS$ is at $U$ (on $TV$ and $ZS$), $\angle YXZ$ is at $X$ (on $WY$ and $ZS$), but they are not between the two lines (exterior - like? No, $\angle YXZ$ is on the opposite side). So not consecutive interior.
• Option 3: $\angle TUS$ and $\angle WXZ$: $\angle TUS$ is at $U$, $\angle WXZ$ is at $X$, not between the two lines.
• Option 4: $\angle WXU$ and $\angle YXZ$: These are not on the same side of the transversal.

Wait, actually, the correct pair is $\angle TUX$ and $\angle WXU$. Wait, let's re - define: Consecutive interior angles are two angles that lie between the two lines (the "interior") and on the same side of the transversal. The transversal here is $ZS$, and the two lines are $WY$ and $TV$. $\angle WXU$ is between $WY$ and $ZS$ (interior), $\angle TUX$ is between $TV$ and $ZS$ (interior), and they are on the same side of $ZS$? Wait, maybe the diagram shows that $WY$ and $TV$ are the two lines cut by transversal $ZS$. So $\angle TUX$ (at $U$, between $TV$ and $ZS$) and $\angle WXU$ (at $X$, between $WY$ and $ZS$) are on the same side of $ZS$ and between the two lines. So they are consecutive interior angles.

Answer:

$\angle TUX$ and $\angle WXU$ (the first option)