Triangle ABC is inscribed in a circle centered at point O. Find the degree measure of the angle

Triangle ABC is inscribed in a circle centered at point O. Find the degree measure of the angle C of triangle ABC if the angle AO is 27 degrees.

Since the triangle ABC is inscribed in a circle, therefore the angle AOB is the central angle resting on the arc AB, and the angle ACB is the inscribed angle resting on the same arc AB. Hence the angle ACB is equal to half of the central angle AOB, that is, the angle ACB = 27˚: 2 = 13.5˚.
Answer: the degree measure of the angle C is 13.5˚.