More infomation is in the image
https://i.stack.imgur.com/xC1Ih.jpg
In case you can't read my handwriting:
GIVENS:
lengths of
BC, CD, DE, EF, GB, GC, GD, GE, GF, DA
angles of
GBC, GCD, GDE, GEF, GFE, BGC, CGD, DGE, EGF, BAC, CAD, DAE, EAF
WE NEED:
Any of the following angles:
ABC, ACD, ADE, AEF, AFE
The only constraint that limits $A$ is the given length of $\overline{DA}$, consequently, $A$ can be anywhere on the circle having that given length as radius, centered on $D$.