The central angle is 82 degrees greater than the inscribed angle, which rests on the same arc. Find these corners.

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 = 82. (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 = 82.

Y = ASB = 82.

X = AOB = Y + 82 = 82 + 82 = 164.

Answer: The center angle is 164, the inscribed angle is 82.