\begin{aligned}

&\text { In } \triangle A C E \\

&\quad A B=B C \text { and } A F=F E \text { (given) } \\

&\quad \therefore B F \| C E \text { and } B F=\frac{1}{2} C E \text { (mid-pt. Th.) } \\

&\text { In } \triangle D F B \\

&\quad F E=E D \text { (given) } \\

&B F \| G E \text { (proven) } \\

&\therefore B G=G D \text { and } G E=\frac{1}{2} B F \\

&\quad(\text { conv. mid-pt. Th.) } \\

&\therefore B F=2 G E \\

&\therefore B F=2(15)=30 \mathrm{~cm} \\

&\quad C E=2 B F \text { (proven) } \\

&\therefore C E=2(30)=60 \mathrm{~cm}

\end{aligned}