MATH SOLVE

2 months ago

Q:
# 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°

Accepted Solution

A:

Answer:m arc EAC=280°Step-by-step explanation:see the attached figure to better understand the problemstep 1Find the measure of arc BCwe know thatm arc EAC=m arc EAB+m arc BC ----> equation Awe havem arc EAB=180° ----> because the line segment BE is a diameterm arc AB+m arc BC+m arc CD=180° ----> because the line segment AB is a diametersubstitute the given values and solve for m arc BC55°+m arc BC+25°=180°80°+m arc BC=180°m arc BC=180°-80°=100°step 2Find the measure of arc EACm arc EAC=m arc EAB+m arc BC ----> equation Awe havem arc EAB=180°m arc BC=100°substitutem arc EAC=180°+100°=280°