The central and inscribed corners rest on the same arc. Find their degree measures if the center angle is 50

The central and inscribed corners rest on the same arc. Find their degree measures if the center angle is 50 degrees greater than the inscribed one.

We know that:
angle ABC = 1/2 arc AC;
angle AOC = arc AC;
This way we can form an equation.
We get an equation of the following form:
arc AC – 50 = 1/2 arc AC;
2 arcs AC – 100 = arc AC;
arc AC = 100 ⇒ angle AOC = 100, angle ABC = 1/2 arc AC = 50;
Answer: angle AOC = 100, angle ABC = 50.