The central angle AOB is 30 degrees greater than the angle inscribed in the circle and resting

The central 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.

Let the value of the central angle AOB be equal to X0, and the value of the inscribed angle ACB equal to Y0.

Then, by hypothesis, X – Y = 30. (1).

Since the value of the inscribed angle is equal to half the value of the central angle, then:

2 * Y = X. (2).

Let us solve the system of two equations 1 and 2 by the substitution method.

2 * Y – Y = 30.

Y = ASB = 30.

X = AOB = Y + 30 = 30 + 30 = 60.

Answer: The center angle is 60, the inscribed angle is 30.