Question: Find $m\angle W$ in rhombus $VWXY$.
$9u+96^\circ$
$4u+58^\circ$
$m\angle W = __^\circ$
1. **State the problem:** We need to find the measure of angle $W$ in rhombus $VWXY$ given the expressions for angles $Y$ and $X$ as $9u+96^\circ$ and $4u+58^\circ$ respectively.
2. **Recall properties of a rhombus:** Opposite angles in a rhombus are equal, and adjacent angles are supplementary (sum to $180^\circ$).
3. **Set up the equation:** Since $Y$ and $X$ are adjacent angles, their measures add up to $180^\circ$:
$$ (9u + 96) + (4u + 58) = 180 $$
4. **Simplify the equation:**
$$ 9u + 96 + 4u + 58 = 180 $$
$$ 13u + 154 = 180 $$
5. **Solve for $u$:**
$$ 13u = 180 - 154 $$
$$ 13u = 26 $$
$$ u = \frac{26}{13} $$
$$ u = 2 $$
6. **Find $m\angle W$:** Since $W$ is opposite $Y$, $m\angle W = m\angle Y = 9u + 96$.
Substitute $u=2$:
$$ m\angle W = 9(2) + 96 = 18 + 96 = 114^\circ $$
**Final answer:**
$$ m\angle W = 114^\circ $$