Question

O is the center of the given circle. The measure of angle O is 128°. The diagram is not drawn to scale.

Assuming that lines that appear to be tangent are tangent, what is the value of x?

Answer 1

The answer is 52°

Hope I helped :)

Answer 2

we know that

The measure of the external angle is the semi difference of the arcs that it covers.
so
see the picture attached to better understand the problem

m AB=128°--------> by central angle
m ACB=360°-128°-----> m ACB=232°
∠x=(1/2)*[m ACB-m AB]
∠x=(1/2)*[232-128]-----> ∠x=(1/2)*104°-----> ∠x=52°

the answer is
∠ x is 52°