Solve for x, y and z with reasons.

The angle $74^\circ$ and angle $y$ are adjacent angles on the straight line AB. Angles on a straight line sum to $180^\circ$.

$$74^\circ + y = 180^\circ$$ $$y = 180^\circ - 74^\circ$$ $$y = 106^\circ$$

Reason: Angles on a straight line (linear pair).

The angle $74^\circ$ and angle $x$ are alternate interior angles. Since lines AB and CD are parallel, alternate interior angles are equal.

$$x = 74^\circ$$

Reason: Alternate interior angles are equal.

Angle $y$ and angle $z$ are alternate interior angles. Since lines AB and CD are parallel, alternate interior angles are equal.

$$z = y$$

Since we found $y = 106^\circ$:

$$z = 106^\circ$$

Reason: Alternate interior angles are equal.

Alternatively for $z$:
The angle $74^\circ$ and angle $z$ are consecutive interior angles (also known as same-side interior angles). Consecutive interior angles sum to $180^\circ$.

$$74^\circ + z = 180^\circ$$ $$z = 180^\circ - 74^\circ$$ $$z = 106^\circ$$

Reason: Consecutive interior angles are supplementary.

The values are:
$x = \boxed{\text{74}^\circ}$
$y = \boxed{\text{106}^\circ}$
$z = \boxed{\text{106}^\circ}$