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

Summary Submit Skip Question

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 \(\triangle{SRU}\):

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