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

280

just did it

Answer 2

m arc EAC=280°

Explanation:

see the attached figure to better understand the problem

step 1

Find the measure of arc BC

we know that

m arc EAC=m arc EAB+m arc BC ----> equation A

we have

m arc EAB=180° ----> because the line segment BE is a diameter

m arc AB+m arc BC+m arc CD=180° ----> because the line segment AB is a diameter

substitute the given values and solve for m arc BC

55°+m arc BC+25°=180°

80°+m arc BC=180°

m arc BC=180°-80°=100°

step 2

Find the measure of arc EAC

m arc EAC=m arc EAB+m arc BC ----> equation A

we have

m arc EAB=180°

m arc BC=100°

substitute

m arc EAC=180°+100°=280°