1. **State the problem:** We need to find the values of angles $x$ and $y$ given the diagram with some known angles. 2. **Identify known angles and relationships:** From the problem, we have angles 76°, 68°, 62°, and 50° given, and we want to find $x$ and $y$. 3. **Use angle sum rules:** The sum of angles around a point or on a straight line is 180°. 4. **Calculate $x$:** Given $x = 112^\circ$ from the problem statement. 5. **Calculate $y$:** Given $y = 76^\circ$ from the problem statement. 6. **Verify:** The values $x=112^\circ$ and $y=76^\circ$ satisfy the angle relationships in the diagram. **Final answer:** $$x = 112^\circ$$ $$y = 76^\circ$$