1. **Problem statement:** Find the measure of angle $\angle V$ in the parallelogram where $m\angle V = 71^\circ$, and given expressions $36x - 1$, $29x + 1$, and $50^\circ$ with $x=2$. 2. **Recall properties of parallelograms:** Opposite angles are equal, and adjacent angles are supplementary (sum to $180^\circ$). 3. **Substitute $x=2$ into the expressions:** $$36x - 1 = 36 \times 2 - 1 = 72 - 1 = 71$$ $$29x + 1 = 29 \times 2 + 1 = 58 + 1 = 59$$ 4. **Check angle relationships:** Since $m\angle V = 71^\circ$ and one adjacent angle is $50^\circ$, check if they sum to $180^\circ$: $$71 + 50 = 121 \neq 180$$ 5. **Check if $36x - 1$ and $29x + 1$ are angles adjacent to $\angle V$:** They sum to: $$71 + 59 = 130 \neq 180$$ 6. **Given $m\angle V = 71^\circ$ and $x=2$, the measure of $\angle V$ is simply:** $$\boxed{71^\circ}$$ This matches the given value and the substitution confirms the expression $36x - 1$ equals $71$ when $x=2$. **Final answer:** $m\angle V = 71^\circ$