1. **State the problem:** We need to find the values of $x$, $y$, and $z$ in a parallelogram with given angles: 2°, $x$°, 121°, 31°, 74°, and $y$°. 2. **Recall properties of parallelograms:** Opposite angles are equal, and adjacent angles are supplementary (sum to 180°). 3. **Given:** $y = 47$°. 4. **Find $x$:** Since $x$ and 2° are adjacent angles on a straight line inside the parallelogram, they sum to 180°. $$x + 2 = 180$$ $$x = 180 - 2 = 178$$ 5. **Find $z$:** The problem does not explicitly mention $z$, but assuming $z$ is the angle adjacent to 121° and 31°, and since adjacent angles in a parallelogram sum to 180°, we can find $z$. $$z + 121 = 180$$ $$z = 180 - 121 = 59$$ 6. **Verify $y$:** Given $y = 47$°, check if it fits the parallelogram properties. Since $y$ and 74° are adjacent angles, $$y + 74 = 180$$ $$47 + 74 = 121 \neq 180$$ This suggests $y$ is not adjacent to 74°, so $y$ is likely opposite to 47°, confirming $y = 47$°. **Final answers:** $$x = 178$$ $$y = 47$$ $$z = 59$$