Please solve the following sum thanks in advance

It is given that x=y and AB=CB

By considering the △ABE


We know that


Exterior ∠AEB=∠EBA+∠BAE


By substituting ∠AEB as y we get


y=∠EBA+∠BAE


By considering the △BCD


We know that


x=∠CBA+∠BCD


It is given that x=y


So we can write it as


∠CBA+∠BCD=∠EBA+∠BAE


On further calculation, we can write it as


∠BCD=∠BAE


Based on both △BCD and △BAE


We know that B is the common point


It is given that AB=BC


It is proved that ∠BCD=∠BAE


Therefore, by ASA congruence criterion we get


△BCD≅△BAE


We know that the corresponding sides of congruent triangles are equal


Therefore, it is proved that AE=CD.