1. **Stating the problem:** We are given a geometric diagram with angles labeled 35°, x°, y°, and 247° at points B, E, F, and C respectively. We need to find the values of angles $x$ and $y$. 2. **Understanding the problem:** The angles around a point sum to 360°. Also, the sum of angles in a triangle is 180°. 3. **Using the angle at point C:** Given angle at C is 247°, the remaining angles around point C must sum to $360° - 247° = 113°$. 4. **Using the triangle at point F:** The angles at F are $y°$ and the adjacent angles. Since EF is a straight line, angles on a straight line sum to 180°. 5. **Using the triangle at point B:** Angle at B is 35°, and angle at E is $x°$. Since EA and BF are lines forming triangles, the sum of angles in triangle EBF is 180°. 6. **Forming equations:** - At point E, angles $x°$ and adjacent angles sum to 180° (straight line). - Triangle EBF: $x + 35 + y = 180$ 7. **Solving for $y$:** $$y = 180 - 35 - x = 145 - x$$ 8. **Using the angle at F and C:** Since $y$ and the angle adjacent to 247° at C form a straight line, $$y + (360 - 247) = 180$$ $$y + 113 = 180$$ $$y = 67$$ 9. **Substitute $y=67$ into $y = 145 - x$:** $$67 = 145 - x$$ $$x = 145 - 67 = 78$$ **Final answers:** $$x = 78°$$ $$y = 67°$$