8.4. In triangle $A B C$, points $E$ and $D$ are on sides $A B$ and $B C$ respectively, such that segments $A D$ and $C E$ are equal, $\angle B A D=\angle E C A$ and $\angle A D C=\angle B E C$. Find the angles of the triangle.
Answer: All angles are $60^{\circ}$.

Triangles $C E A$ and $A D B$ are equal (by side and adjacent angles). Therefore, sides $A C$ and $A B$ are equal, and angles $C A E$ and $A B D$ are equal, which means angles $C A B$ and $A B C$ are equal. This implies the equality of sides $A C$ and $B C$. Thus, triangle $A B C$ is equilateral.