Since the inscribed angle ACB and the central angle AOB rest on the same arc AB, the angle AOB is twice the angle ACB.
AOB = 2 * ACB. (1)
By condition, the angle AOB is 78 more than the angle ACB.
AOB = ACB + 78. (2)
Let’s solve the system of equations 1 and 2.
ACD + 78 = 2 * ACD.
ASB = 78.
Then the angle AOB = 2 * 78 = 156.
Answer: The value of the angle AOB is 156.
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