Question

which angles are vertical angles? (image of lines and angles) ∠sru and ∠tuw, ∠srp and ∠qru, ∠srp and ∠vur, ∠vuw and ∠qrp

Explanation:

Step1: Recall vertical angles definition

Vertical angles are opposite angles formed by two intersecting lines, they are equal and share a common vertex.

Step2: Analyze each option

• Option 1: $\angle SRU$ and $\angle TUW$: Check if they are opposite at intersection. No, not vertical.
• Option 2: $\angle SRP$ and $\angle QRU$: These are opposite angles formed by intersecting lines $WP$ and $QS$ (or $WP$ and $TV$? Wait, lines $WP$ (through U and R) and QS (through R and Q/S) intersect at R? Wait, no, lines $WP$ (with points W, U, R, P) and QS (Q, R, S) intersect at R? Wait, no, line $WP$ intersects line $TV$ at U and line $QS$ at R? Wait, no, looking at the diagram: line $WP$ (with arrows W← and P→) passes through U (on TV) and R (on QS). Line $TV$ is vertical (T↑, V↓), line $QS$ is vertical (Q↑, S↓). So when line $WP$ intersects line $QS$ at R, and line $WP$ intersects line $TV$ at U. Wait, vertical angles at intersection of two lines: when two lines intersect, they form two pairs of vertical angles. So at point R, lines $WP$ and $QS$ intersect? Wait, no, line $WP$ is a transversal crossing two vertical lines $TV$ and $QS$. Wait, maybe I misread. Wait, the lines: $TV$ (vertical, T top, V bottom), $QS$ (vertical, Q top, S bottom), and $WP$ (slanted, W left, P right) crossing $TV$ at U and $QS$ at R. So at point R, the lines are $WP$ (W-P) and $QS$ (Q-S). So when two lines intersect (WP and QS at R), the vertical angles would be $\angle SRP$ (at R, between S-R and R-P) and $\angle QRU$ (at R, between Q-R and R-U). Wait, yes! Because $\angle SRP$ and $\angle QRU$ are opposite angles formed by the intersection of lines $WP$ and $QS$ (or $WP$ and the line through Q-R-S). Wait, no, line $QS$ is vertical, line $WP$ is slanted. So at their intersection (point R), the two angles opposite each other are $\angle SRP$ (below QS, above WP? Wait, no, let's visualize: at point R, line QS goes up (Q) and down (S), line WP goes left (U, then W) and right (P). So the angle between S-R and R-P is $\angle SRP$, and the angle between Q-R and R-U is $\angle QRU$. These are vertical angles because they are opposite at the intersection of WP and QS. Let's check other options:
• Option 3: $\angle SRP$ and $\angle VUR$: $\angle VUR$ is at U, not R. Different vertices, so not vertical.
• Option 4: $\angle VUW$ and $\angle QRP$: Different vertices (U and R), not vertical.

So $\angle SRP$ and $\angle QRU$ are vertical angles.

Answer:

$\angle SRP$ and $\angle QRU$ (the second option, e.g., if options are labeled as:
A. $\angle SRU$ and $\angle TUW$
B. $\angle SRP$ and $\angle QRU$
C. $\angle SRP$ and $\angle VUR$
D. $\angle VUW$ and $\angle QRP$

Then the answer is B. $\angle SRP$ and $\angle QRU$)