The provided diagram for polygon PQRSTU appears to have conflicting information regarding chord lengths and angles.

This problem contains contradictory information within the diagram and markings.

1. The chords $PQ, QR, RS, ST, TU, UP$ are all marked with a single dash, which typically indicates they are all equal in length.
2. If all chords are equal, then the polygon $PQRSTU$ is a regular hexagon.
3. In a regular hexagon inscribed in a circle, each central angle (e.g., $\angle POQ$, $\angle QOR$) is $360^\circ / 6 = 60^\circ$.
4. If $\angle QOR = 60^\circ$, then since $OQ=OR$ (radii), $\triangle OQR$ is an equilateral triangle. Thus, $\angle