1. **State the problem:** Given a circle with points T, S, R, Q on its circumference and angles $m\angle STQ = 246^\circ$ and $m\angle TSR = 123^\circ$, find: (a) $m\angle STQ$ (already given as 246°) (b) $m\angle TQR$ 2. **Recall the rule for angles in a circle:** - The measure of an inscribed angle is half the measure of its intercepted arc. - The sum of angles around a point is $360^\circ$. 3. **Analyze the given angles:** - $m\angle STQ = 246^\circ$ is likely the measure of the arc $SQ$ intercepted by angle $STQ$. - $m\angle TSR = 123^\circ$ is the measure of angle $TSR$. 4. **Find $m\angle TQR$:** - Since $T, S, R, Q$ lie on the circle, quadrilateral $TSQR$ is cyclic. - Opposite angles in a cyclic quadrilateral sum to $180^\circ$. - $m\angle TSR + m\angle TQR = 180^\circ$ - Substitute $m\angle TSR = 123^\circ$: $$m\angle TQR = 180^\circ - 123^\circ = 57^\circ$$ 5. **Final answers:** (a) $m\angle STQ = 246^\circ$ (b) $m\angle TQR = 57^\circ$