#### Answer

m$\angle$RQS = 43$^{\circ}$
m$\angle$TQS = 137$^{\circ}$

#### Work Step by Step

$\angle$RQS and $\angle$TQS are supplementary angles, meaning they equal 180$^{\circ}$ when added together. To solve, add the two equations together, set them equal to 180, and then solve for the variable:
(6x + 20) + (2x + 4) = 180$^{\circ}$
8x + 24 = 180$^{\circ}$
8x = 156$^{\circ}$
x = 19.5$^{\circ}$
Now, plug this x value back into the original equations:
m$\angle$RQS = 2x +4 = 2(19.5) + 4 = 39 + 4 = 43$^{\circ}$
m$\angle$TQS = 6x + 20 = 6(19.5) + 20 = 117 + 20 = 137$^{\circ}$