Question: Find the measure of the arc.
m\u2322ACB = [?]\u00b0
146\u00b0
position_hint: center
Graph: two concentric circles with center at the same point, three radii drawn to points C (top), A (right), and B (lower-left), with a central angle marked 146\u00b0 between the right ray and lower-left ray; the outer arc from A to B passing through C is the major arc ACB.
1. **State the problem:** We need to find the measure of the major arc $\overset{\frown}{ACB}$ given the central angle $146^\circ$ between points $A$ and $B$.
2. **Recall the rule:** The measure of a major arc is $360^\circ$ minus the measure of the minor arc (or central angle) between the same two points.
3. **Apply the formula:**
$$\text{Measure of major arc } \overset{\frown}{ACB} = 360^\circ - 146^\circ$$
4. **Calculate:**
$$360^\circ - 146^\circ = 214^\circ$$
5. **Conclusion:** The measure of the major arc $\overset{\frown}{ACB}$ is $214^\circ$.