Question

which angles are corresponding angles?
∠tsq and ∠wvs ∠tsq and ∠wvx
∠tsq and ∠uvs ∠tsq and ∠rsv

Explanation:

Step1: Recall Corresponding Angles Definition

Corresponding angles are in the same relative position at each intersection where a transversal crosses two parallel lines. They are equal when lines are parallel.

Step2: Analyze Each Option

• Option 1: ∠TSQ and ∠WVS

Check positions. ∠TSQ is at S (transversal XQ, line RT), ∠WVS at V (transversal XQ, line UW). Not same relative position.

• Option 2: ∠TSQ and ∠WVX

∠WVX is at V (transversal XQ, line UW), ∠TSQ at S. Different positions (one is on transversal, one at intersection).

• Option 3: ∠TSQ and ∠UVS

∠UVS is at V (transversal XQ, line UW, upper-left), ∠TSQ at S (transversal XQ, line RT, lower-right). Not corresponding.

• Option 4: ∠TSQ and ∠RSV

Wait, re - evaluate. Wait, correct analysis: ∠TSQ and ∠WVX? No, wait, let's re - look. Wait, the correct corresponding angles: ∠TSQ and ∠WVX? No, wait, the transversal is XQ, cutting lines UW and RT. ∠WVX is at V (on line UW, transversal XQ, angle at V between XQ and UW, upper - left), ∠TSQ is at S (on line RT, transversal XQ, angle at S between XQ and RT, lower - right). Wait, no, the correct pair is ∠TSQ and ∠WVX? Wait, no, the first option: ∠TSQ and ∠WVS. Wait, no, let's use the definition: corresponding angles are in the same "corner" relative to the transversal and the parallel lines. So, for transversal XQ, and parallel lines UW and RT. ∠WVX (at V, on UW, above transversal, left of UW) and ∠TSQ (at S, on RT, below transversal, right of RT)? No, that's not. Wait, maybe I made a mistake. Wait, the correct answer is ∠TSQ and ∠WVX? No, the options: the second option is ∠TSQ and ∠WVX. Wait, let's check the positions again. The transversal is XQ, intersecting UW at V and RT at S. ∠WVX is the angle at V, between XQ (going from X to Q) and WV (part of UW, going down from V to W). ∠TSQ is the angle at S, between XQ (going from X to Q) and TS (part of RT, going down from S to T). So, they are in the same relative position: both are below the transversal, and on the right - hand side of their respective parallel lines (UW and RT). So ∠TSQ and ∠WVX are corresponding angles. Wait, but the options: the second option is ∠TSQ and ∠WVX. Wait, maybe my initial analysis was wrong. Let's re - check each option:

1. ∠TSQ and ∠WVS: ∠WVS is at V, between XQ and WV (but WV is downward, XQ is crossing, so ∠WVS is maybe above? No, WV is from V down to W, so ∠WVS is at V, between XQ (coming from X to V) and WV (going to W). ∠TSQ is at S, between XQ (coming from X to S) and TS (going to T). Not same position.

1. ∠TSQ and ∠WVX: ∠WVX is at V, between XQ (coming from X to V) and WV (going to W)? No, ∠WVX is at V, between XQ (from X to V) and WV (from V to W)? Wait, XQ is the transversal, with X on the left, Q on the right. So at V, the angle ∠WVX is between XQ (X - V - Q) and WV (V - W, downward). At S, ∠TSQ is between XQ (X - S - Q) and TS (S - T, downward). So both are below the transversal, and on the "right" side of their lines (UW and RT). So they are corresponding angles.

1. ∠TSQ and ∠UVS: ∠UVS is at V, between XQ (X - V - Q) and UV (V - U, upward). So it's above the transversal, while ∠TSQ is below. Not corresponding.

1. ∠TSQ and ∠RSV: ∠RSV is at S, between XQ (X - S - Q) and RS (S - R, upward). So it's above the transversal, ∠TSQ is below. Not corresponding.

So the correct pair is ∠TSQ and ∠WVX, which is the second option.

Answer:

∠TSQ and ∠WVX (the option labeled "∠TSQ and ∠WVX")