1. **State the problem:** We need to find the measure of angle $R$ at the center of the circle. 2. **Analyze the given information:** The circle has three radii from the center forming three angles around the center point. - One angle is $32^\circ$ (between the left slanted radius and the horizontal base). - Another angle is $50^\circ$ (between the downward radius and the right-lower radius). - Angle $R$ is between the left slanted radius and the downward radius. 3. **Recall the rule:** The sum of angles around a point is $360^\circ$. 4. **Set up the equation:** Let the three central angles be $32^\circ$, $R$, and $50^\circ$. Then, $$ 32^\circ + R + 50^\circ = 360^\circ $$ 5. **Solve for $R$:** $$ R = 360^\circ - 32^\circ - 50^\circ $$ $$ R = 360^\circ - 82^\circ = 278^\circ $$ 6. **Interpretation:** Angle $R$ measures $278^\circ$ around the center, but since central angles in a circle are usually considered as the smaller angle between two radii, the smaller angle is $$ 360^\circ - 278^\circ = 82^\circ $$ 7. **Conclusion:** The measure of angle $R$ is $82^\circ$. **Final answer:** $\boxed{82^\circ}$