1. **Stating the problem:** We have a geometric figure with angles 144° at E, and a triangle EFG with angles $y^\circ$ at F and $x^\circ$ at G. We need to find $x$ and $y$. 2. **Understanding the angles:** The line from A to E to F forms a straight line with an angle of 144° at E. Since a straight line measures 180°, the adjacent angle at E on the other side is: $$180^\circ - 144^\circ = 36^\circ$$ 3. **Triangle angle sum rule:** In triangle EFG, the sum of interior angles is always 180°: $$x + y + \text{angle at E} = 180^\circ$$ 4. **Finding angle at E in triangle EFG:** The angle at E in triangle EFG corresponds to the 36° angle found in step 2. 5. **Setting up the equation:** $$x + y + 36^\circ = 180^\circ$$ 6. **Simplify to find relationship between x and y:** $$x + y = 180^\circ - 36^\circ = 144^\circ$$ 7. **Additional information needed:** Since the problem does not provide more data, we assume triangle EFG is isosceles with angles $x$ and $y$ equal, or that $x$ and $y$ are complementary in some way. Without loss of generality, if $x = y$, then: $$2x = 144^\circ \Rightarrow x = 72^\circ, y = 72^\circ$$ **Final answer:** $$x = 72^\circ, y = 72^\circ$$