In the figure below, AD is a tangent to the circle ABC, |AB| = |AC| and BAC = 2x^. Find DAC.

Given that $|AB| = |AC|$, triangle ABC is an isosceles triangle. The base angles opposite the equal sides are equal, so $\angle ABC = \angle ACB$.
The sum of angles in a triangle is $180^\circ$.
We are given $\angle BAC = 2x^\circ$.
Therefore,

$$\angle ABC + \angle ACB + \angle BAC = 180^\circ$$ $$2 \angle ABC + 2x^\circ = 180^\circ$$ $$2 \angle ABC = 180^\circ - 2x^\circ$$ $$\angle ABC = \frac{180^\circ - 2x^\circ}{2}$$ $$\angle ABC = (90 - x)^\circ$$

The Alternate Segment Theorem states that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
In this figure, AD is the tangent to the circle at point A, and AC is a chord through the point of contact A.
The angle between the tangent AD and the chord AC is $\angle DAC$.
The angle in the alternate segment subtended by the chord AC is $\angle ABC$.
According to the theorem, these angles are equal:

$$\angle DAC = \angle ABC$$

Substitute the value of $\angle ABC$ found in Step 1 into the equation from Step 2:

$$\angle DAC = (90 - x)^\circ$$

Comparing this result with the given options, it matches option D.

The final answer is $\text{D. } (90 - x)^\circ$.