From the figure, it is not very clear whether x is the measure of angle ACB or of angle ACD.

If x is the measure of angle ACB, then statement 1 is sufficient only as y and x are the measures of alternate interior angles. Hence, x = y = 50

The correct answer will be A.

But if x is the measure of angle ACD, then statement none of the statements are individually sufficient. Only both statements together we can determine the value of x as (180 - y - z) = (180 - 90) = 90

The correct answer will be C.

rahulvsd wrote:If ACD is x, then A can still be sufficient. As ACD and CAD are interior angles on the same side of the transversal and they are supplementary.

Refer to the following diagram,


Angle ACO and angle CAD are interior angles on the same side of the transversal and they are supplementary not angle ACD and angle CAD.

A simple fact that you've ignored:
angle ACD and angle CAD are the two angles of same triangle. If they are supplementary, then their sum will be equal to 180 degrees. That means the measure of the third angle, i.e. angle ADC will be zero. This in turn means the point D will lie on the line segment AC, which is not possible according to the figure given.