The segment BE splits the triangle ABC into nuclei similar to the triangle ABE

The segment BE splits the triangle ABC into nuclei similar to the triangle ABE and BCE, and the coefficient of similarity is equal to √3. Find the corners of the triangle.

Given:
triangle ABC,
segment BE splits triangle ABC into two similar triangles ABE and BCE,
BE / AE = BE / EC = AB / BC = √3.
Find the angles of triangles ABE and BCE -?
Decision:
We know that in such triangles the corresponding angles are equal to each other.
Therefore, the angle BEA = angle BEC,
angle ABE = angle EBC,
angle BAE = angle BSE.
Answer: angle BEA = angle BEC, angle ABE = angle EBC, angle BAE = angle BCE.