1. **State the problem:** We need to find the measure of the major arc $XZY$ in circle $C$. The given arcs are $120^\circ$ and $40^\circ$. 2. **Understand the arcs:** The circle's total circumference is $360^\circ$. The minor arcs given are $120^\circ$ and $40^\circ$. 3. **Formula:** The measure of the major arc is the total circle minus the sum of the minor arcs. 4. **Calculate the sum of minor arcs:** $$120^\circ + 40^\circ = 160^\circ$$ 5. **Calculate the major arc $XZY$:** $$360^\circ - 160^\circ = 200^\circ$$ 6. **Answer:** The measure of arc $XZY$ is $200^\circ$.