1. **Problem statement:** We have points A, B, C, D, and E on a circle with given angles 26°, 52°, and 125°, and unknown angles $x$ and $y$. We need to find $x$ and $y$. 2. **Key rule:** The sum of opposite angles in a cyclic quadrilateral is 180°. 3. **Step 1:** Identify cyclic quadrilaterals and use the property. Assuming quadrilateral ABCE is cyclic, then: $$x + 125 = 180$$ 4. **Step 2:** Solve for $x$: $$x = 180 - 125 = 55$$ 5. **Step 3:** For $y$, consider triangle or cyclic quadrilateral involving $y$ and known angles. If $y$ and 26° are opposite angles in a cyclic quadrilateral, then: $$y + 26 = 180$$ 6. **Step 4:** Solve for $y$: $$y = 180 - 26 = 154$$ 7. **Step 5:** If $z$ is the remaining angle in triangle with angles $x$, $y$, and $z$, use triangle sum: $$x + y + z = 180$$ Substitute $x=55$, $y=154$: $$55 + 154 + z = 180$$ 8. **Step 6:** Solve for $z$: $$z = 180 - 209 = -29$$ Negative angle is impossible, so $z$ must be in a different triangle or configuration. 9. **Step 7:** If $z$ is supplementary to 52° (on circle), then: $$z + 52 = 180$$ 10. **Step 8:** Solve for $z$: $$z = 180 - 52 = 128$$ **Final answers:** $$x = 55^6$$ $$y = 154^6$$ $$z = 128^6$$