Question

select all the pairs of alternate exterior angles. ∠wvx and ∠rsq, ∠wvx and ∠uvs, ∠uvx and ∠tsq, ∠wvs and ∠wvx

Explanation:

Step1: Recall Alternate Exterior Angles Definition

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

Step2: Analyze Each Pair

• For $\angle WVX$ and $\angle RSQ$: $\angle WVX$ is outside the two parallel lines ( $UVW$ and $RST$ ) and on one side of transversal $XQ$, $\angle RSQ$ is outside the two lines and on the opposite side of the transversal. So this is a pair of alternate exterior angles.
• For $\angle WVX$ and $\angle UVS$: $\angle UVS$ is inside the two lines, so not exterior. Eliminate.
• For $\angle UVX$ and $\angle TSQ$: $\angle UVX$ is outside the two lines on one side of transversal, $\angle TSQ$ is outside on the opposite side. This is a pair of alternate exterior angles.
• For $\angle WVS$ and $\angle WVX$: These are adjacent angles, not alternate exterior. Eliminate.

Answer:

$\angle WVX$ and $\angle RSQ$, $\angle UVX$ and $\angle TSQ$