2. A triangle can be divided into two isosceles triangles. One of the interior angles of the original triangle is $36^{\circ}$, find all possible values of the largest interior angle of the original triangle.
2. Let's assume $\angle B=36^{\circ}$.
(1) If the dividing line does not pass through point $B$. Let's assume the dividing line is $A D$, at this time, $\triangle B A D$ is a $\left(36^{\circ}, 36^{\circ}, 108^{\circ}\right)$ or $\left(36^{\circ}, 72^{\circ}, 72^{\circ}\right)$ triangle.

If $\triangle B A D$ is a $\left(36^{\circ}, 36^{\circ}, 108^{\circ}\right)$ triangle, then $\triangle C A D$ is either $\left(144^{\circ}, 18^{\circ}, 18^{\circ}\right)$ (as shown in Figure 8(a)), or $\left(72^{\circ}, 54^{\circ}, 54^{\circ}\right)$ (as shown in Figure 8(b)), or $\left(36^{\circ}, 72^{\circ}, 72^{\circ}\right)$ (as shown in Figures 8(c) and (d)).
(2) If the dividing line passes through point $B$. Let's assume it is $B E$, then, $\triangle A B E$ must be $\left(132^{\circ}, 24^{\circ}, 24^{\circ}\right)$, and $\triangle C B E$ is a $\left(156^{\circ}, 12^{\circ}, 12^{\circ}\right)$ triangle (as shown in Figure 9).
Therefore, the largest interior angle of the original triangle could be $72^{\circ}, 90^{\circ}, 108^{\circ}, 126^{\circ}, 132^{\circ}$.