1. **Problem Statement:** We have a quadrilateral ABCD with opposite sides parallel (AB \parallel DC and AD \parallel BC). Angles at vertices A, B, D are $x^\circ$, $y^\circ$, and $z^\circ$ respectively, and the angle at vertex C is $104^\circ$. We need to find $x$, $y$, and $z$. 2. **Key Property:** Since ABCD is a parallelogram (opposite sides parallel), opposite angles are equal, and adjacent angles are supplementary (sum to $180^\circ$). 3. **Using the property of opposite angles:** - Angle $x$ at A equals angle $z$ at D because they are opposite angles. 4. **Using the property of adjacent angles:** - Angles at C and D are adjacent, so $z + 104 = 180$. 5. **Calculate $z$:** $$z = 180 - 104 = 76$$ 6. **Since $x = z$, then:** $$x = 76$$ 7. **Angles at A and B are adjacent, so:** $$x + y = 180$$ 8. **Calculate $y$:** $$y = 180 - x = 180 - 76 = 104$$ **Final answers:** $$x = 76^\circ, \quad y = 104^\circ, \quad z = 76^\circ$$