1. **Problem statement:** Find the measures of angles $m\angle WRZ$ and $m\angle XWY$ given that $m\angle H = (8x - 2)^\circ$ and the context involves trapezoids and quadrilaterals. 2. **Understanding the problem:** Typically, in trapezoids and quadrilaterals, the sum of interior angles is $360^\circ$. Also, adjacent angles on a straight line sum to $180^\circ$. 3. **Given data:** - Quadrilateral $PQRS$ with $m\angle P = 104^\circ$, $m\angle R = 41^\circ$. - Angles $m\angle Q$ and $m\angle S$ are unknown. 4. **Find $m\angle Q$ and $m\angle S$:** Using the sum of interior angles of a quadrilateral: $$m\angle P + m\angle Q + m\angle R + m\angle S = 360^\circ$$ Substitute known values: $$104 + m\angle Q + 41 + m\angle S = 360$$ Simplify: $$145 + m\angle Q + m\angle S = 360$$ $$m\angle Q + m\angle S = 360 - 145 = 215$$ 5. **Find $m\angle WRZ$ and $m\angle XWY$:** Assuming $m\angle WRZ$ and $m\angle XWY$ are related to $m\angle H = (8x - 2)^\circ$, and that these angles are supplementary or part of a linear pair, we need more information or equations to solve for $x$ and then find these angles. 6. **Since no further data is provided, we express $m\angle WRZ$ and $m\angle XWY$ in terms of $x$ or given expressions.** **Final answers:** - $m\angle Q + m\angle S = 215^\circ$ - $m\angle H = (8x - 2)^\circ$ - $m\angle WRZ$ and $m\angle XWY$ require additional information to solve. **Note:** Please provide more details or relationships between these angles to find exact measures.