The chord AB divides the circle with the center O into two arcs, the ratio of which is 5: 7.

The chord AB divides the circle with the center O into two arcs, the ratio of which is 5: 7. Find the value of the central angle AOB (in degrees), based on the smaller of the arcs AB.

Let the degree measure of the smaller arc AB = 5 * X0, then the degree measure of the larger arc AB = 7 * X0.

The sum of the larger and smaller arcs AB is a circle, the degree measure of which is 360.

Then 5 * X + 7 * X = 360.

12 * X = 360.

X = 360/12 = 30.

Then the smaller arc AB = 5 * 30 = 150.

The central angle AOB resting on the smaller arc AB is equal to the degree measure of this arc.

Angle AOB = 150.

Answer: Angle AOB is 150.