The center angle AOB is 30 degrees greater than the angle inscribed in the circle and resting on the arc AB.

The center angle AOB is 30 degrees greater than the angle inscribed in the circle and resting on the arc AB. Find the values of these angles.

The degree measure of the inscribed angle resting on the arc AB is two times less than the central angle resting on the same arc.
Let the angle ACB = X0, then the angle ABO = 2 * ACB = 2 * X, and by condition, AOB – ACB = 30, 2 * X – X = 30.
X = ACB = 30, angle ABO = 2 * 30 = 60.
Answer: The inscribed angle is 30, the center angle is 60.