1. **Problem statement:** Find the measure of the unknown arc or angle indicated in the circle with given angles 52° and 121°. 2. **Relevant formula:** In a circle, the sum of angles around a point is 360°. Also, the measure of an arc opposite an inscribed angle is related by the formula: the measure of the arc intercepted by the angle is twice the angle measure. 3. **Given:** Angle at point F is 52°, arc SR is 121°. 4. **Step:** Since angle F intercepts arc SR, the measure of angle F is half the measure of arc SR if angle F is an inscribed angle. But here, angle F is 52°, and arc SR is 121°, which is consistent because 2 * 52° = 104°, which is not equal to 121°, so angle F is not the inscribed angle for arc SR. 5. **Step:** The unknown angle or arc is opposite to these points. The total circle is 360°, so the unknown arc or angle can be found by subtracting the known arcs or angles from 360°. 6. **Calculate unknown arc:** $$\text{Unknown arc} = 360^\circ - 121^\circ - 52^\circ = 360^\circ - 173^\circ = 187^\circ$$ 7. **Answer:** The measure of the unknown arc or angle is $187^\circ$.