1. **Problem:** Find the intercepted arcs and angle measures for points on the circle with points R, Q, S, T and center P. 2. **Formula and rules:** - The measure of an inscribed angle is half the measure of its intercepted arc: $$m\angle = \frac{1}{2} m\overset{\frown}{arc}$$ - The measure of an arc is the degree measure of the central angle that intercepts it. 3. **Step a:** For $\angle S$, it intercepts arc $RQ$ because $\angle S$ is formed by points R and Q on the circle. 4. **Step b:** Given $m\angle R = 37^\circ$, use the inscribed angle formula: $$m\angle R = \frac{1}{2} m\overset{\frown}{SQ} \Rightarrow m\overset{\frown}{SQ} = 2 \times 37 = 74^\circ$$ 5. **Step c:** Given arc $RT = 60^\circ$, find arc $RQ$ by subtracting arc $RT$ from the full circle 360°: $$m\overset{\frown}{RQ} = 360 - 60 - m\overset{\frown}{SQ} = 360 - 60 - 74 = 226^\circ$$ **Final answers:** - a) $\angle S$ intercepts arc $RQ$, $m\angle S = 30^\circ$ (assuming from diagram or problem context) - b) $\angle R$ intercepts arc $SQ$, $m\overset{\frown}{SQ} = 74^\circ$ - c) $m\overset{\frown}{RQ} = 226^\circ$