In triangle $CAT$, we have $\angle ACT =\angle ATC$ and $\angle CAT = 36^\circ$. If $\overline{TR}$ bisects  $\angle ATC$, then $\angle CRT =$

$\text{(A)}\ 36^\circ\qquad\text{(B)}\ 54^\circ\qquad\text{(C)}\ 72^\circ\qquad\text{(D)}\ 90^\circ\qquad\text{(E)}\ 108^\circ$
In $\triangle ACT$, the three angles sum to $180^\circ$, and $\angle C = \angle T$
$\angle CAT + \angle ATC + \angle ACT = 180$
$36 + \angle ATC + \angle ATC = 180$
$2 \angle ATC = 144$
$\angle ATC = 72$
Since $\angle ATC$ is bisected by $\overline{TR}$, $\angle RTC = \frac{72}{2} = 36$
Now focusing on the smaller $\triangle RTC$, the sum of the angles in that triangle is $180^\circ$, so:
$\angle RTC + \angle TCR + \angle CRT = 180$
$36 + \angle ACT + \angle CRT = 180$
$36 + \angle ATC + \angle CRT = 180$
$36 + 72 + \angle CRT = 180$
$\angle CRT = 72^\circ$, giving the answer $\boxed{C}$