In the diagram, RTS=28^ , VRM=46^ , MQ is a tangent to the circle VRSTU at the point R. Find VUS.

The Alternate Segment Theorem states that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
Given that $MQ$ is a tangent to the circle at $R$ and $VR$ is a chord, $\angle VRM$ is the angle between the tangent $MR$ and the chord $VR$. The angle subtended by the chord $VR$ in the alternate segment is $\angle VUR$.

Given $\angle VRM = 46^\circ$.

The Angles in the Same Segment Theorem states that angles subtended by the same arc at the circumference are equal.
Given $\angle RTS = 28^\circ$. This angle is subtended by the arc $RS$.
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