Question

In circle O, and are diameters. The measure of arc AB is 55° and the measure of arc CD is 25°.

Circle O is shown. Line segments A D and B E are diameters. Line segments O F and O C are radii.

What is the measure of Arc E A C?

100°
125°
235°
280°

Answer 1

Since AD and BE are diameters, arc AD = arc BE = 180°.

Given arc AB = 55°, arc AE = arc BE − arc AB = 180° − 55° = 125°.

Given arc CD = 25° and arc AD = 180°, arc AC = arc AD − arc CD = 180° − 25° = 155°.

Arc EAC = arc EA + arc AC = 125° + 155° = 280°.

Answer: 280°.