angles ptq and str are vertical angles and congruent. which arcs are congruent? sp and sr pq and sr pq and…

Answer:

$\overset{\frown}{PQ}$ and $\overset{\frown}{SR}$

Explanation:

Step1: Recall the central - angle - arc relationship

In a circle, if two central angles are congruent, then the arcs they intercept are congruent.

Step2: Identify the central angles and their intercepted arcs

Given that $\angle PTQ$ and $\angle STR$ are vertical angles (and thus congruent). $\angle PTQ$ intercepts arc $\overset{\frown}{PQ}$, and $\angle STR$ intercepts arc $\overset{\frown}{SR}$. Since the central angles $\angle PTQ\cong\angle STR$, by the central - angle - arc congruence theorem (in a circle, congruent central angles intercept congruent arcs), we can conclude that $\overset{\frown}{PQ}\cong\overset{\frown}{SR}$.