Let the value of the angle AOB be equal to 17 * X0, then, by condition, the value of the angle BOC will be equal to 19 * X0.
Since the sum of adjacent angles is 180, then (17 * X + 19 * X) = 180.
36 * X = 180.
X = 180/35 = 5.
Then the angle AOB = 17 * 5 = 85, the angle BOC = 19 * 5 = 95.
Answer: The larger angle is 95.
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