AB is the diameter of a circle centered at the point O, BC is a chord. It is known that the angle AOC = 130 °.

AB is the diameter of a circle centered at the point O, BC is a chord. It is known that the angle AOC = 130 °. Find the degree measures of the angles of the AOC triangle.

It is necessary to find the degree measures of the angles of the AOC triangle.
AB is the diameter of a circle centered at point O, which means that AO = BO; AO, ВO are radii, but OС is also a radius. And the radii of the same circle are equal
AO = OC, therefore, triangle AOC is isosceles, and the angles at the base of such triangles are equal, therefore the angle OAC = angle OCA
The angles in a triangle add up to 180 °.
Then
OAC angle + OCA angle + AOC angle = 180 °
2 * angle OAC + 130 ° = 180 °
2 * OAC angle = 180 ° -130 °
2 * angle OAC = 50
angle OAC = 50 ° / 2
angle OAC = 25 °
Answer: angle AOC = 130 °, angle OAC = 25 °, angle OCA = 25 °.