1. **Problem:** Find the measure of angle $\angle YZV$ given arcs and angles in a circle. 2. **Formula:** The measure of an inscribed angle is half the measure of its intercepted arc. 3. **Given:** Arc $YZ = 144^\circ$, another arc or angle also $144^\circ$. 4. **Calculation:** $$m\angle YZV = \frac{144^\circ + 144^\circ}{2} = \frac{288^\circ}{2} = 144^\circ$$ 5. **Explanation:** Since the angle intercepts arcs totaling $288^\circ$, the angle measure is half of that. **Final answer:** $m\angle YZV = 144^\circ$