Thread: Need help: a question on triangle geometry

[Refer to the attachment for picture]

Given an isoscles triangle ABC where AB = AC.
angle BAC = 20 (degrees)
angle EBC = 60
angle DCB = 50

Find angle DEB.

Hint: produce 2 other straight lines within triangle ABC.

Method being tried:
prove triangle ABE = isoscles
produce a line GE with G as a point on AD; assume GE = DE
prove triangles AGE and BDE = congruent (AAS)
prove GE // DC (not done yet...)
hence angle AEG = angle ACD = 30 (degrees)
hence angle DEB = 30 (degrees)
OR
produce the same line GE and assume that GE // DC, then prove triangle AGE congruent to BDE....

Thanks.