Answer: 105 degrees
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Work Shown:
Inscribed angle theorem
arc measure = 2*(inscribed angle)
arc BCD = 2*(angle A)
arc BCD = 2*(59)
arc BCD = 118 degrees
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arc BCD combines with minor arc AB to get
(minor arc AB)+(arc BCD) = (137)+(118) = 255
Subtract this from 360 to get
360 - 255 = 105
This is the measure of minor arc AD as this is the missing portion to form a full circle.
In other words,
(minor arc AD) + (arc BCD) + (minor arc AB) = 105 + 118 + 137 = 360