Question

(overrightarrow{tv}) and (overrightarrow{wy}) are parallel lines. which angles are alternate interior angles? ( angle tux ) and ( angle yxu ) ( angle vus ) and ( angle tux ) ( angle vus ) and ( angle vux ) ( angle vus ) and ( angle yxu )

Explanation:

Step1: Recall the definition of alternate interior angles

Alternate interior angles are formed when a transversal crosses two parallel lines. They lie between the two parallel lines and on opposite sides of the transversal.

Step2: Analyze each option

• For \(\angle TUX\) and \(\angle YXU\):

They lie between the parallel lines \(WY\) and \(TV\) and on opposite sides of the transversal \(ZS\).

• For \(\angle VUS\) and \(\angle TUX\): \(\angle VUS\) and \(\angle TUX\) are vertical angles (not alternate - interior angles).
• For \(\angle VUS\) and \(\angle VUX\): \(\angle VUS\) and \(\angle VUX\) are adjacent angles (not alternate - interior angles).
• For \(\angle VUS\) and \(\angle YXU\): \(\angle VUS\) and \(\angle YXU\) are not in the correct position (not between the two parallel lines in the alternate - interior sense).

Answer:

\(\angle TUX\) and \(\angle YXU\)