In the diagram, m vert vert vert TSR = 52^ vert. What is m vert vert vert RST?

The problem states that $m\angle TSR = 52^\circ$.

The angle $\angle RST$ refers to the angle with vertex S, formed by the rays SR and ST. This is the same angle as $\angle TSR$, where the vertex is S and the rays are ST and SR. The order of the non-vertex letters does not change the angle itself.

Since $\angle RST$ is the same angle as $\angle TSR$, its measure is also $52^\circ$.

The angle $RST$ is $\boxed{\text{}52^\circ\text{}}$