Calculate the interior angle at the vertex with the reflex angle.

A full circle measures $360^\circ$. The interior angle of the triangle at that vertex is the difference between $360^\circ$ and the given reflex angle.

The sum of the interior angles of any triangle is $180^\circ$. The three interior angles of this triangle are $x$, $x$, and $150^\circ$.

Subtract $150^\circ$ from both sides:

Divide by 2:

The size of angle $x$ is $\boxed{\text{15}^\circ}$.