Answer:
C
Step-by-step explanation:
There are only 3 perhaps 4. A central angle must have its vertex at the center of a circle. That means that the middle letter naming the angle must be O.
The two obvious ones without any argument are <AOB and <BOC
The question is what about <AOC. It qualifies as well. If it is a diameter then the answer is 3. If it is not a diameter but 2 radii meeting at the center then there are 4. <AOC has a major and minor arc. <OBC is not a central angle.
A is wrong. It contains <OBC.
B is wrong. Same Reason
C is correct. <AOC is a central angle
D is incomplete and therefore wrong.
