1. **Problem statement:** We have a quadrilateral OPQR inscribed in circle S. The interior angles at vertices O and P are given as 97° and 101° respectively. We need to find the measure of angle $\angle R$. 2. **Key property:** In a cyclic quadrilateral (one inscribed in a circle), opposite angles sum to 180°. That is, $\angle O + \angle Q = 180^\circ$ and $\angle P + \angle R = 180^\circ$. 3. **Given:** $\angle O = 97^\circ$, $\angle P = 101^\circ$. 4. **Find:** $\angle R$. 5. **Use the property for angles P and R:** $$\angle P + \angle R = 180^\circ$$ 6. Substitute $\angle P = 101^\circ$: $$101^\circ + \angle R = 180^\circ$$ 7. Solve for $\angle R$: $$\angle R = 180^\circ - 101^\circ$$ $$\angle R = 79^\circ$$ 8. **Answer:** The measure of $\angle R$ is $79^\circ$.