1. **State the problem:** We have a parallelogram ABCD with angles labeled as follows: $\angle A = 65^\circ$, $\angle B = x^\circ$, $\angle C = y^\circ$, and $\angle D = z^\circ$. We need to find the values of $x$, $y$, and $z$. 2. **Recall properties of parallelograms:** In any parallelogram, opposite angles are equal, and adjacent angles are supplementary (sum to 180 degrees). 3. **Apply these properties:** - Since $\angle A = 65^\circ$, then $\angle C = y = 65^\circ$ because opposite angles are equal. - Adjacent angles sum to 180 degrees, so $\angle A + \angle B = 180^\circ$ which means $65 + x = 180$. - Similarly, $\angle B + \angle C = 180^\circ$ and $\angle D + \angle A = 180^\circ$. But since $\angle C = 65^\circ$, $\angle B = x$, and $\angle D = z$, we can find $x$ and $z$. 4. **Calculate $x$:** $$65 + x = 180$$ $$x = 180 - 65$$ $$x = 115$$ 5. **Calculate $z$:** Since $\angle D$ is opposite to $\angle B$, $z = x = 115^\circ$. 6. **Summary of angles:** - $x = 115^\circ$ - $y = 65^\circ$ - $z = 115^\circ$ **Final answer:** $$x = 115^\circ, \quad y = 65^\circ, \quad z = 115^\circ$$