Find the measures of angles x, y, and z.

Angle $x$ and the $68^\circ$ angle form a linear pair on a straight line. Angles on a straight line sum to $180^\circ$.

$$x + 68^\circ = 180^\circ$$ $$x = 180^\circ - 68^\circ$$ $$x = 112^\circ$$

Angle $z$ and the $85^\circ$ angle form a linear pair on a straight line. Angles on a straight line sum to $180^\circ$.

$$z + 85^\circ = 180^\circ$$ $$z = 180^\circ - 85^\circ$$ $$z = 95^\circ$$

Angle $y$ and the $27^\circ$ angle form a linear pair on a straight line. Angles on a straight line sum to $180^\circ$.

$$y + 27^\circ = 180^\circ$$ $$y = 180^\circ - 27^\circ$$ $$y = 153^\circ$$

The measures are:
$x = \boxed{\text{112}^\circ}$
$y = \boxed{\text{153}^\circ}$
$z = \boxed{\text{95}^\circ}$