Segment Areas

Determine the measure of the central angle of a circle that will make the shaded region’s area 1/ 4 of the entire circle’s area.



A red shaded region is sliced off a circle when it is divided by a segment that has endpoints on the circle.

What is the measure of the central angle of the circle (blue) that will make the shaded region’s area 1/4 of the entire circle’s area?