The central angle of a circle is 50 degrees greater than the inscribed angle, resting

The central angle of a circle is 50 degrees greater than the inscribed angle, resting on the same arc. Find the degree measure of the arc.

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 = 50. (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 = 50.

Y = ASB = 50.

X = Y + 50 = 50 + 50 = 100.

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 100.