Points $A,$ $B,$ and $C$ are placed on a circle centered at $O$ as in the following diagram:

If AC = BC and angle OAC = 18 degrees then how many degrees are in angle AOB?

Draw radius OC

And since OC = OA, then angles OCA and OAC are equal

Then angle COA = 180 - 18 -18 = 180 - 36 = 144°

And by symmetry, angle BOC = 144°

So angle AOB = 360 - 144 - 144 = 360 - 288 = 72°