Answer: Option A.
Step-by-step explanation:
The angle ∠QST and the angle ∠QSR are supplementary.
If two angles are supplementary, means that the sum of both angles is 180 degrees.
Thenrefore
[tex]QST+QSR=180\°[/tex]
Solve for the angle ∠QSR and substitute the value of the angle ∠QST to find the value of the angle ∠QSR. Then, solving the equation, you get:
[tex]QSR=180\°-QST\\QSR=180\°-150\°\\\\QSR=30\°[/tex]
Then [tex]tan(QSR)[/tex] is:
[tex]tan(30\°)=\frac{\sqrt{3}}{3}[/tex]
This matches with the option A.
