1. **State the problem:** We have a parallelogram ABCD with angles at vertices A and D labeled as $(x + 40)^\circ$ and $(x - 40)^\circ$ respectively. We need to find the value of $x$. 2. **Recall properties of parallelograms:** Opposite angles in a parallelogram are equal, and adjacent angles are supplementary (sum to $180^\circ$). 3. **Apply the supplementary angle rule:** Since angles A and D are adjacent, their measures add up to $180^\circ$: $$ (x + 40) + (x - 40) = 180 $$ 4. **Simplify the equation:** $$ x + 40 + x - 40 = 180 $$ $$ 2x = 180 $$ 5. **Solve for $x$:** $$ x = \frac{180}{2} = 90 $$ 6. **Conclusion:** The value of $x$ is $90$ degrees.