The sum of the angles AOC and ABC = 96 °. Find the angle ABC if O is the center of the circle.

According to the condition of the problem, two angles are given, each of which rests on one arc of the AC.
Consider these angles:
The AOC angle is the central angle, its degree measure will be equal to the degree measure of the AC arc.
Angle ABC is an inscribed angle and will be equal to half of the arc on which the central angle AOC rests.
We introduce a variable and denote the degree measure of the angle ABC x, then the angle AOC is 2x. We get the equation:
x + 2x = 96 °
3x = 96 °
x = 32 °.
Answer: the angle ABC is 32 °.