Find the value of x in the figure below a) 94 b) 78 c) 110° d) 210

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

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.