1. **Problem Statement:** Find the value of $x$ in the parallelogram $ABCD$ where angle $B$ is $34^\circ$ and angle $D$ is $x$. 2. **Key Property:** In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (sum to $180^\circ$). 3. **Apply the property:** Since $ABCD$ is a parallelogram, angle $B$ and angle $D$ are opposite angles, so: $$x = 34^\circ$$ 4. **Verification:** Adjacent angles $B$ and $C$ sum to $180^\circ$, and since angles $C$ and $A$ are equal (given by arcs), this confirms the parallelogram properties. **Final answer:** $$\boxed{34^\circ}$$