Question

The figure below shows a triangle with vertices A and B on a circle and vertex C outside it. Side AC is tangent to the circle. Side BC is a secant intersecting the circle at point X.

Answer 1

What is the measure of angle ACB?

Answer 2

try this: http://tinypic.com/view.php?pic=2z3rihh&s=6

Answer 3

Angle C is an angle formed by a secant and a tangent from a point outside the circle.
Its measure is given by the formula 1/2 the difference of the outer and inner arcs cut off by the angle.
M<C = 1/2 (156 - 64) = 46 -->
The 64 for the inner arc comes from doubling inscribed angle A with measure 1/2 its intercepted arc. So if the angle is 32, then arc XA is 64. Note that the outer arc AB is given to be 156.