Question

select all the pairs of corresponding angles. ∠tus and ∠tux ∠vus and ∠yxu ∠vux and ∠yxu ∠wxu and ∠tus

Explanation:

Step1: Recall Corresponding Angles Definition

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

Step2: Analyze Each Pair

• ∠TUS and ∠TUX: These share a common side and vertex, not corresponding (adjacent or same - side, not relative position from transversal and parallel lines).
• ∠VUS and ∠YXU: Line \(WX\parallel TV\) (parallel lines) and transversal \(ZS\). ∠VUS and ∠YXU are in the same relative position (below the transversal, on the right - hand side of their respective parallel lines), so they are corresponding angles.
• ∠VUX and ∠YXU: These are alternate interior angles (between parallel lines, on opposite sides of transversal), not corresponding.
• ∠WXU and ∠TUS: Line \(WX\parallel TV\) (parallel lines) and transversal \(ZS\). ∠WXU and ∠TUS are in the same relative position (above the transversal, on the left - hand side of their respective parallel lines), so they are corresponding angles.

Answer:

\(\angle VUS\) and \(\angle YXU\), \(\angle WXU\) and \(\angle TUS\)