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°
2 answers:
Answer:
m arc EAC=280°
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
<em>Find the measure of arc BC</em>
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
<em>Find the measure of arc EAC</em>
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°
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