Triangle ABC is inscribed in a circle centered at point O. Angle A is 28 degrees, angle C is 22 degrees. Find the AOC angle?

Two angles of the triangle ABC are known by condition, we find the third angle B:
∠ B = 180 ° – (∠ A + ∠ C) = 180 ° – (28 ° + 22 °) = 130 °.
We got that triangle ABC is obtuse, the center of the circumscribed circle – point O will be located outside this triangle.
The central angle AOC rests on the arc ABC or the sum of the arcs AB and BC. The inscribed angle C rests on the arc AB, the inscribed angle A rests on the arc BC.
We find the degree measure of the central angle of the AOC:
∠ AOC = 2 * (∠ A + ∠ C) = 100 °.
Answer: The central angle AOC is 100 °.