1. **State the problem:** We need to find the measure of angle $\angle Y$ in rhombus $WXYZ$ where $m\angle Y = c$ and $m\angle Z = 2c + 24^\circ$. 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 $\angle Y$ and $\angle Z$ are adjacent angles, we have: $$c + (2c + 24) = 180$$ 4. **Simplify the equation:** $$c + 2c + 24 = 180$$ $$3c + 24 = 180$$ 5. **Isolate $c$:** $$3c = 180 - 24$$ $$3c = 156$$ 6. **Divide both sides by 3:** $$\cancel{3}c = \frac{156}{\cancel{3}}$$ $$c = 52$$ 7. **Find $m\angle Y$:** Since $m\angle Y = c$, $$m\angle Y = 52^\circ$$ **Final answer:** $m\angle Y = 52^\circ$