There's the tangent secant angle theorem which says the measure of angle B is half the difference of the two intercepted arcs. That means
58 = (1/2) (210 - x)
116 = 210 - x
x = 94
Answer: A
That's not a very intuitive answer. Let's see if we can see why. Let's call the center of the circle O and the unlabeled intersection at the top D.
Angle DOC=210 degrees the long way, that's what an arc measure means
Angle DOC=360-210=150 degrees the short way
We have angle BCO=90 degrees because it's a tangent.
So angle BDO is the fourth angle in a quadrailateral BCDO
BDO = 360 - DBC - BCO - DOC = 360 - (58 + 150+90) = 62 degrees
ADO is isosceles, with two radii for sides. So DAO=62 degrees
That leaves DOA = 180 - 62 - 62 = 56 degrees
Angle AOC = x
x + arc AD = DOC
x + 56 = 150
x = 94
That checks.
