To find the measure of arc \( AC \) given that the measure of \( \angle CBA \) is \( 66^\circ \), we can use the relationship between an inscribed angle and the arc it subtends.
The measure of an arc is twice the measure of the inscribed angle that subtends that arc. Since \( \angle CBA \) subtends arc \( AC \), we can use the following formula:
\[ \text{measure of arc } AC = 2 \times \text{measure of } \angle CBA \]
Substituting the given measure of \( \angle CBA \):
\[ \text{measure of arc } AC = 2 \times 66^\circ = 132^\circ \]
Therefore, the measure of arc \( AC \) is \( \boxed{132} \) degrees.
1 answer