The measure of the central angle AOB is by 30° greater than the measure of the inscribed angle which intercepts arc AB. What are the measures of these angles?

inscribed angle: 30° central angle: 60°

Step-by-step explanation:

The central angle is double the inscribed angle for the same intercepted arc. Since doubling the angle adds 30° to it, the original inscribed angle must be 30°.

Then the central angle is 30°+30° = 2·30° = 60°.