1. **Stating the problem:** We have a parallelogram with angles labeled $y^\circ$, $3y^\circ$, and $3x^\circ$. We want to find the values of $x$ and $y$. 2. **Recall properties of parallelograms:** Opposite angles are equal, and adjacent angles are supplementary (sum to $180^\circ$). 3. **Set up equations:** Since $y^\circ$ and $3y^\circ$ are adjacent angles, they must satisfy: $$y + 3y = 180$$ which simplifies to: $$4y = 180$$ 4. **Solve for $y$:** $$y = \frac{180}{4} = 45$$ 5. **Use the other angle $3x^\circ$:** Since $3x^\circ$ is adjacent to $y^\circ$, they also sum to $180^\circ$: $$y + 3x = 180$$ Substitute $y=45$: $$45 + 3x = 180$$ 6. **Solve for $x$:** $$3x = 180 - 45 = 135$$ $$x = \frac{135}{3} = 45$$ 7. **Final answer:** $$x = 45^\circ, \quad y = 45^\circ$$