In $\triangle{RST}$ below, $U$ is a point on $\overline{RT}$ such that $\overrightarrow{SU}$ is an angle bisector of $\angle{RST}$. What is $m\angle{R}$ ?

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We can add up the angles in $\triangle{SUT}$:

$$x+3x+x+5=180$$ $$5x+5 = 180$$ $$5(x+1) = 180$$ $$x+1 = 36$$ $$x= 35$$

$\angle{RUS}$ is supplemental to $\angle{SUT}$.

$$\angle{RUS} + \angle{SUT} = 180$$ $$\angle{RUS} + 3x = 180$$ $$\angle{RUS} + 3(35) = 180$$ $$\angle{RUS} + 105 = 180$$ $$\angle{RUS} = 75$$

We can then sum up the angles of $\triangle{SRU}$:

$$35+75 + \angle{R} = 180$$ $$110 + \angle{R} = 180$$ $$\angle{R} = \boxed{70^\circ}$$