1. **Stating the problem:** Find the values of the variables $x$ and $y$ in the cyclic quadrilateral $RSTQ$ where the angles are $x^\circ$ at $R$, $y^\circ$ at $S$, $80^\circ$ at $T$, and $95^\circ$ at $Q$. 2. **Formula used:** In a cyclic quadrilateral, opposite angles sum to $180^\circ$. That is, $$\text{Angle}_1 + \text{Angle}_3 = 180^\circ$$ $$\text{Angle}_2 + \text{Angle}_4 = 180^\circ$$ 3. **Apply the rule to find $x$:** $$x + 80 = 180$$ $$x = 180 - 80$$ $$x = 100$$ 4. **Apply the rule to find $y$:** $$y + 95 = 180$$ $$y = 180 - 95$$ $$y = 85$$ 5. **Final answer:** $$x = 100^\circ, \quad y = 85^\circ$$