1. **State the problem:** We need to find the measure of angle $\angle RST$ in triangle $SRT$ inscribed in a circle with center $Q$. 2. **Given information:** The central angle $\angle SQR$ measures 111°. 3. **Recall the rule:** The measure of an inscribed angle is half the measure of the intercepted arc or central angle. 4. **Apply the rule:** Since $\angle RST$ is an inscribed angle that intercepts the same arc as the central angle $\angle SQR$, its measure is half of 111°. 5. **Calculate:** $$\angle RST = \frac{1}{2} \times 111 = 55.5$$ 6. **Final answer:** $m\angle RST = 55.5^\circ$