Final answer:
Vertical angles are the angles opposite each other when two lines intersect. Without a specific diagram, it's challenging to confirm which option correctly identifies the vertical angles. Based on the naming convention, Option 3 ∠TRV and ∠WRU could be vertical angles, as they may share common vertices R and W and could be formed by intersecting lines. Option 3 is correct.
Step-by-step explanation:
A pair of vertical angles are the angles that are opposite each other when two lines intersect. To determine which option represents a pair of vertical angles, we need to visualize or refer to the intersecting lines that form the angles mentioned in each option.
Without the specific diagram, it is challenging to confidently identify the correct pair of vertical angles. However, typically, vertical angles share the same vertex and are formed by the same two lines that intersect. The labels of the angles often reflect this relation, with the vertex letter being in the middle of the three-letter notation of each angle, and the first and last letters being interchangeable.
Option 1: ∠VRU and ∠SRT do not form vertical angles because they do not have a common vertex and the lines forming them seem to be different based on the names.
Option 2: ∠TRS and ∠VRW also do not share a common vertex; thus, they cannot be vertical angles.
Option 3: ∠TRV and ∠WRU, by their labels, appear to have the potential to form vertical angles because they share vertices R and W and could be formed by intersecting lines if T, V, W, and U are points on those lines.
Option 4: ∠WRV and ∠SRW; this option does not likely form vertical angles, because despite sharing vertex R, the angle names suggest that the angles are not formed by the same intersecting lines.