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.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.