Explanation:
Since no other info is given, you would use a protractor, centered at O. Read off the degree measure, to the nearest degree (a high quality protractor may have divisions to a quarter of a degree). Arc AC has that many degrees.
If the angle is ABC, where B is also on the circle, this is called an inscribed angle, with vertex (its”point”) at B. Now, arc AC will have exactly twice the degree measure of angle ABC. That is a theorem in geometry textbooks, which has been known for about 2500 years!