Identify the properties of OQR.

O is the center of the circle, so OQ and OR are radii.
Therefore, $OQ = OR$, which means $\triangle OQR$ is an isosceles triangle.
In an isosceles triangle, the base angles are equal: $\angle OQR = \angle ORQ$.
From the diagram, $\angle QOR = x$ and $\angle ORQ = y$.
The problem states "If TQ = TR and $x = 120^\circ$". Based on the diagram, $x$ refers to the central angle $\angle QOR$.

The sum of angles in $\triangle