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Circle O has tangent AB and secant AC as shown. arc BC measures 4x+2-. arc BE measures 2x-10. What is the measure of arc CB

Circle O has tangent AB and secant AC as shown arc BC measures 4x2 arc BE measures 2x10 What is the measure of arc CB class=

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Answer:

b. 160°

Step-by-step explanation:

angle A = (far arc - near arc)/2

far arc is  arc BC and near arc is arc BE. Replacing into the equation:

∠A = (arc BC - arc BE)/2

50 = [4x + 20 - (2x - 10)]/2

50*2 = 2x + 30

x = (100 - 30)/2

x = 35°

Replacing this information into arc BC equation:

arc BC = 4(35) + 20 = 160°