Answer: 82 degrees
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Work Shown:
The four pieces, or arcs, of the circle add up to 360 degrees. Use this fact to find the measure of minor arc AD.
(minor arc AD) + (minor arc DC) + (minor arc CB) + (minor arc BA) = 360
(minor arc AD) + (120) + (100) + (96) = 360
(minor arc AD) + 316 = 360
minor arc AD = 360-316
minor arc AD = 44 degrees
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Combine minor arcs AD and DC to form arc ADC
arc ADC = (minor arc AD) + (minor arc DC)
arc ADC = (44) + (120)
arc ADC = 164 degrees
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Lastly, use the inscribed angle theorem
inscribed angle = (1/2)*(arc measure)
angle B = (1/2)*(arc ADC)
angle B = (1/2)*(164)
angle B = 82 degrees
