Question 788896
∠ RQS and ∠ TQS are vertical angles


so that means they are congruent (since vertical angles are congruent)


so set them equal, plug in the given expressions, then solve for x


m ∠ RQS = m ∠ TQS 


3(x + 7) = 4x + 15


3x+21 = 4x+15


3x = 4x+15-21


3x-4x = 15-21


-x = 15-21


-x = -6


x = (-6)/(-1)


x = 6


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Since x = 6, we know that 


m ∠ RQS =  3(x + 7)


m ∠ RQS =  3(6 + 7)


m ∠ RQS =  3(13)


m &#8736; RQS =  <font color="red">39 degrees</font>


Angle TQS is also 39 degrees (since the two angles are congruent vertical angles). I'll let you determine angle TQS (plug x = 6 into the second equation and evaluate).