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°

m arc EAC=280°

Step-by-step 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°