① when DA=DE

∠DEA=( 180-40)/2=70

∴∠dec= 180-70= 1 10

∠∠C =∠B = 40。

∴∠ecd= 180-40- 1 10=30

∴∠adb= 180-40-30= 1 10

That is, when ∠ ADB = 1 10, △ADE is an isosceles triangle.

② when AD=AE.

AED =∠ ade =40

∫∠AED is the outer corner of △ dec.

∴∠EDC+∠C=∠AED=40

∠∠C =∠B = 40。

∴∠EDC does not exist, and △EDC does not exist.

At this time, d coincides with b or c.

When d and c coincide, points d, e, a, e and a do not form a triangle.

When d and b coincide, △ADE is an isosceles triangle, but there is no △ ∠ADB.

That is, when ∠ADB=0, △ADE is an isosceles triangle.

I don't know if D can coincide with B.C. If not, it doesn't exist.

③ when EA=ED

∠AED= 180-40-40= 100

∫∠AED is the outer corner of △ dec.

∴∠EDC+∠C= 100

..... (you know)

∴∠EDC=60

∴∠ADB= 180-60-40=80

That is, when ∠ ADB = 80, △AED is an isosceles triangle.

(End)