Points A, B, C lie on a circle centered at point O. Arc AB refers to arc AC as 2: 3.

Points A, B, C lie on a circle centered at point O. Arc AB refers to arc AC as 2: 3. Arc AB 180 °, arc AC 180 °, angle BAC = 55 °. What is the AOC angle?

The inscribed angle BAC = 550 and rests on the BC arc, then the degree measure of the BC arc = 2 * 55 = 110.

The sum of the degree measures of arcs AB and AC is equal to: AB + AC = (360 – BC) = (360 – 110) = 250.

Let the degree measure of the arc AB = 2 * X0, then the arc AC = 3 * X0.

2 * X + 3 * X = 250.

5 * X = 250.

X = 250/5 = 50.

Then the arc AC = 3 * 50 = 150.

The central angle AOC rests on the arc AC, then the angle AOC is equal to the degree measure of the arc.

Angle AOC = 150.

Answer: The AOC angle is 150.