Given a parallelogram $ABCD$ in which $\angle ABD=90^\circ$ and $\angle CBD=45^\circ$. Point $E$ lies on segment $AD$ such that $BC=CE$. Determine the measure of angle $BCE$.
Source: 2022 Polish Junior Math Olympiad Finals P3
Tags: geometry
Given a parallelogram $ABCD$ in which $\angle ABD=90^\circ$ and $\angle CBD=45^\circ$. Point $E$ lies on segment $AD$ such that $BC=CE$. Determine the measure of angle $BCE$.
