Question

angles
angles ptq and str are vertical angles and congruent.
which arcs are congruent?

Explanation:

Step1: Recall vertical - angle and arc relationship

In a circle, if two central angles (or inscribed angles subtended by the same arcs) are congruent, the arcs they intercept are congruent. Since angles PTQ and STR are vertical angles and congruent, the arcs they intercept are congruent. Angle PTQ intercepts arc PQ and angle STR intercepts arc SR.

Answer:

$\overparen{PQ}$ and $\overparen{SR}$