This problem contains contradictory information within the diagram and markings.
- The chords PQ,QR,RS,ST,TU,UP are all marked with a single dash, which typically indicates they are all equal in length.
- If all chords are equal, then the polygon PQRSTU is a regular hexagon.
- In a regular hexagon inscribed in a circle, each central angle (e.g., ∠POQ, ∠QOR) is 360∘/6=60∘.
- If ∠QOR=60∘, then since OQ=OR (radii), △OQR is an equilateral triangle. Thus, $\angle