The central angle is 68 degrees larger than the inscribed one. Determine the degree measure

The central angle is 68 degrees larger than the inscribed one. Determine the degree measure of the arc on which they rest.

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 = 68. (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 = 68.

Y = AСB = 68.

X = Y + 68 = 68 + 68 = 136.

The degree measure of an arc is equal to the degree measure of the central angle that rests on this arc.

Answer: The degree measure of the arc is 136.