1. **State the problem:** We have a parallelogram TUWV with angles at vertices U and V given as $(x + 158)^\circ$ and $(x + 74)^\circ$ respectively. We need to find the measure of angle $V$, i.e., $m\angle V$. 2. **Recall properties of parallelograms:** Opposite angles are equal, and adjacent angles are supplementary (sum to $180^\circ$). 3. **Set up the equation:** Since angles $U$ and $V$ are adjacent, their measures add up to $180^\circ$: $$ (x + 158) + (x + 74) = 180 $$ 4. **Simplify the equation:** $$ 2x + 232 = 180 $$ 5. **Isolate $x$:** $$ 2x = 180 - 232 $$ $$ 2x = -52 $$ 6. **Divide both sides by 2:** $$ x = \frac{\cancel{2}x}{\cancel{2}} = \frac{-52}{2} $$ $$ x = -26 $$ 7. **Find $m\angle V$ by substituting $x$ back:** $$ m\angle V = x + 74 = -26 + 74 = 48^\circ $$ **Final answer:** $m\angle V = 48^\circ$