The measure of the $\measuredangle EAD$ where $E$ is outside the square $ABCD$

Question

For reference:

Let the squares $ABCD$ and $FGDE$ such that E, G and C are collinear, $GE = GC$, Calculate the measure of the $\measuredangle EAD$ where $E$ is outside the square $ABCD$.(answer: 18.5 $^\circ$)

My progress..

I was able to draw the figure but I don't know there is some restriction…in geogebra the solution matches

Answer 1

Draw $AJ \parallel CE$ such that $AJ = CE$. Use symmetry about diagonal $AC$.

$\triangle ACE$ is a well known right triangle with perpendicular sides in the ratio $1:2$. The angles are $26.5^\circ$ and $63.5^\circ$.

So, $\angle EAD = \angle 63.5^\circ - 45^\circ = 18.5^\circ$

Here is another observation. Points $A, B, J, C, D$ and $E$ are all concyclic with center at $O$.

Here is a complete diagram with $9$ squares.