1.33*. Segment $B E$ divides triangle $A B C$ into two similar triangles, with the similarity coefficient being $\sqrt{3}$. Find the angles of triangle $A B C$.

## §3. Ratio of Areas of Similar Triangles
1.33. Since $\angle A E B + \angle B E C = 180^{\circ}$, these angles cannot be different angles of similar triangles $A B E$ and $B E C$, i.e., they are equal and $B E$ is a perpendicular.

There are two possible cases: $\angle A B E = \angle C B E$ or $\angle A B E = \angle B C E$. The first case is ruled out, as in this case $\triangle A B E = \triangle C B E$. The second case remains. In this case, $\angle A B C = \angle A B E + \angle C B E = \angle A B E + \angle B A E = 90^{\circ}$. In the right triangle $A B C$, the legs are in the ratio $1: \sqrt{3}$, so its angles are $90^{\circ}, 60^{\circ}, 30^{\circ}$.