Using only elementary geometry, determine angle x.
You may not use trigonometry, such as sines and cosines, the law of sines, the law of cosines, etc.
Now, it's easy to prove that CE=AG, and DF=DG=GF. Since AF=CF, then EF=GF.
Then EF=DF $\Rightarrow$ $\angle$FED=$\angle$FDE.
While $\angle$DFE=$\angle$ABC=80$^\circ$, so $\angle$DEF=50$^\circ$.
From $\angle$AEB=30$^\circ$, we can get x=$\angle$DEA=20$^\circ$. [Q.E.D]
This is known as the problem of "adventitious angles". You'll find many references if you search the web for that phrase.