Question

tv and wy are parallel lines.
diagram of two parallel lines tv and wy cut by a transversal sz, with points t, u, v on tv and w, x, y on wy, and s, u, x, z on the transversal
which angles are corresponding angles?
∠tux and ∠yxz
∠yxu and ∠vus
∠vus and ∠tus
∠tux and ∠vux

Explanation:

Step1: Recall Corresponding Angles Definition

Corresponding angles are equal when two parallel lines are cut by a transversal. They occupy the same relative position at each intersection.

Step2: Analyze Each Option

• Option 1: $\angle TUX$ and $\angle YXZ$: $\angle YXZ$ is a vertical angle or not in corresponding position. Eliminate.
• Option 2: $\angle YXU$ and $\angle VUS$: Since $TV \parallel WY$ and $SZ$ is transversal, $\angle YXU$ (at $WX$ intersection) and $\angle VUS$ (at $TV$ intersection) are in corresponding positions (above the parallel line, same side of transversal).
• Option 3: $\angle VUS$ and $\angle TUS$: These are supplementary (linear pair), not corresponding. Eliminate.
• Option 4: $\angle TUX$ and $\angle VUX$: These are supplementary (linear pair), not corresponding. Eliminate.

Answer:

$\angle YXU$ and $\angle VUS$ (the second option: $\boldsymbol{\angle YXU}$ and $\boldsymbol{\angle VUS}$)