Construction Is A Piece Of Cake, Right? (Part-2)

Akshat influenced by Anshuman and took an arbitrary $\bigtriangleup ABC$ and started doing aimless constructions, the steps of which are given below-

($1$) He extended $AB$ to a point $D$ such that $AD=BC$.

($2$) Then he constructed an $\angle ECB$ which is equal to $\angle ABC$ ($E$ being any point lying on the opposite side of $AD$).

($3$) He then joined $BE$ and $DC$ which meet each other at $X$.

($4$) Then he joined $AX$ which intersects $EC$ at $F$.

($5$) Next, he joined $AE$ and drew parallel to it from $F$ which meets $AC$ at $G$.

Akshat then wondered what $BG$ could possibly be equal to?