Question

which angles are alternate exterior angles? (image of intersecting lines with points q, r, s, t, u, v, w, p; options: ∠srp and ∠vur, ∠srp and ∠qru, ∠qrp and ∠vur, ∠tuw and ∠srp)

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 Option

• Option 1: $\angle SRP$ and $\angle VUR$: $\angle SRP$ is outside the lines $QS$ and $TV$, $\angle VUR$ is inside? No, wait, let's check positions. Wait, transversal is $PW$. Lines $QS$ and $TV$ are parallel? Assuming they are. $\angle TUW$ and $\angle SRP$: $\angle TUW$ is outside (below $TV$ and left of transversal), $\angle SRP$ is outside (above $QS$ and right of transversal)? Wait no, let's re - check. Wait the correct alternate exterior angles: $\angle TUW$ and $\angle SRP$: $\angle TUW$ is at the lower intersection, outside the two lines (below $TV$ and left of transversal $PW$), $\angle SRP$ is at the upper intersection, outside the two lines (above $QS$ and right of transversal $PW$), and they are on opposite sides of the transversal. Let's check other options:
• $\angle SRP$ and $\angle VUR$: $\angle VUR$ is inside the two lines, so not exterior.
• $\angle SRP$ and $\angle QRU$: $\angle QRU$ is adjacent, not alternate exterior.
• $\angle QRP$ and $\angle VUR$: $\angle QRP$ is a straight - line angle with $\angle SRP$, and $\angle VUR$ is inside, so no.

So the correct pair is $\angle TUW$ and $\angle SRP$.

Answer:

$\angle TUW$ and $\angle SRP$ (the option with $\angle TUW$ and $\angle SRP$)