Calculate the size of angle x.

Step 1: Identify that angles $Z$ and $150^\circ$ are adjacent angles on a straight line.

$Z + 150^\circ = 180^\circ$

Step 2: Subtract $150^\circ$ from both sides.

$Z = 180^\circ - 150^\circ$

Step 3: Simplify.

$Z = 30^\circ$

The size of angle $Z$ is $\boxed{30^\circ}$.