Find the value of x in the diagram? (adjacent and vertical angles)

It's a diagram. --> http://i55.tinypic.com/3354ffn.png

I don't get this. My answer would be
x^2 = 64 + 36
x^2 = 100
x = sqrt100
x = 10

But my teacher said it's wrong. So what's the correct answer?

According to the figure, I think your answer is correct.

Im not sure if the (x^2)* is referring to that one angle or both. If it is both then you are right.
If is is just that one then:
x^2 and 64* are vertical angles so
x^2 = 64
x = sqrt64
x = 6*

x^2=64 since vertically opposite angles
x=8 or x=-8