Question

select all the pairs of vertical angles.
∠vwy and ∠xwt
∠utr and ∠vwt
∠vwt and ∠xwy
∠xwt and ∠stw

Explanation:

Step1: Recall vertical - angle definition

Vertical angles are formed when two lines intersect. They are opposite each other and are congruent.

Step2: Analyze the intersection at point W

At the intersection of lines VX and RY at point W, $\angle VWY$ and $\angle XWT$ are vertical angles because they are opposite each other. Also, $\angle VWT$ and $\angle XWY$ are vertical angles.

Step3: Analyze the intersection at point T

At the intersection of lines SU and RY at point T, $\angle UTR$ and $\angle VWT$ are vertical angles (since they are opposite each other). Also, $\angle XWT$ and $\angle STW$ are vertical angles.

Answer:

$\angle VWY$ and $\angle XWT$, $\angle UTR$ and $\angle VWT$, $\angle VWT$ and $\angle XWY$, $\angle XWT$ and $\angle STW$