Find the center angle AOB if it is 78 degrees greater than the inscribed angle ACB resting on the same arc.

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.