1. **State the problem:** We are given two line segments VW and UX with lengths expressed as $y - 49$ and $y - 64$ respectively. We need to find the value of $y$. 2. **Analyze the figure and given information:** The quadrilateral VWXT has a diagonal UX. Since the problem gives lengths VW and UX in terms of $y$, and asks for $y$, it suggests these lengths might be equal or related. 3. **Assumption:** If VW and UX are equal (which is a common scenario in such problems), then: $$y - 49 = y - 64$$ 4. **Solve the equation:** Subtract $y$ from both sides: $$-49 = -64$$ This is false, so VW and UX cannot be equal. 5. **Alternative approach:** Since the problem does not specify any other relation, and the figure shows UX as a diagonal inside the quadrilateral, the problem might imply that the lengths VW and UX are equal for the quadrilateral to be valid or for some property to hold. 6. **Re-examine the problem:** If VW and UX are equal, then: $$y - 49 = y - 64$$ This is impossible unless $-49 = -64$, which is false. 7. **Conclusion:** Without additional information or constraints, the problem cannot be solved as stated. Possibly, the problem expects us to set the lengths equal to find $y$. 8. **If the problem expects the lengths to be equal, then:** $$y - 49 = y - 64$$ No solution. 9. **If the problem expects the lengths to be equal to a specific value, or if the problem is incomplete, please provide more information.**