The center angle is 28 degrees greater than the inscribed angle resting on the same arc.

The center angle is 28 degrees greater than the inscribed angle resting on the same arc. Find the degree measure for each of the angles.

By the condition of the problem, we are given two angles based on the same arc.
The central angle is equal to the degree measure of the arc, and the degree measure of the inscribed angle is half the arc on which it rests. We introduce the variable x and denote the inscribed angle, then the degree measure of the central angle is 2x.
According to the condition, it is said that the central one is 28 ° more than the inscribed one, we get the equation:
2x – x = 28
x = 28 ° – inscribed angle;
2 * 28 ° = 56 ° is the central angle.
Answer: 28 ° and 56 ° are the degrees of the inscribed and central angles, respectively.