1. **Problem Statement:** We have a quadrilateral STUV inscribed in circle W. We are given four angles: 116° at S, 82° at T, (6x - 28)° at U, and (y + 33)° at V. We need to find the values of $x$ and $y$. 2. **Key Property:** For a quadrilateral inscribed in a circle, the opposite angles are supplementary, meaning their measures add up to 180°. 3. **Set up equations using opposite angles:** - Angles at S and U are opposite, so: $$116 + (6x - 28) = 180$$ - Angles at T and V are opposite, so: $$82 + (y + 33) = 180$$ 4. **Solve for $x$:** $$116 + 6x - 28 = 180$$ $$\Rightarrow 6x + (116 - 28) = 180$$ $$\Rightarrow 6x + 88 = 180$$ $$\Rightarrow 6x = 180 - 88$$ $$\Rightarrow 6x = 92$$ Show cancellation: $$\Rightarrow \cancel{6}x = \cancel{6}\frac{92}{6}$$ $$\Rightarrow x = \frac{92}{6} = \frac{46}{3} \approx 15.33$$ 5. **Solve for $y$:** $$82 + y + 33 = 180$$ $$\Rightarrow y + 115 = 180$$ $$\Rightarrow y = 180 - 115$$ $$\Rightarrow y = 65$$ 6. **Final answers:** $$x = \frac{46}{3} \approx 15.33$$ $$y = 65$$