Because ∠ CDA =180-∠ c-∠ CAD =180-2 ∠ C.

∠CDA = 180-∠ADB = 180-∠b。

And the above two formulas can get ∠B=2∠C=80 degrees.

So ∠BAD= 180-80-80=20 degrees.

2. Because: △ABC and △ADE are equilateral triangles, AB=AC, AE=AD, ∠CAB=∠DAE=60 degrees.

∠CAB =∠BAD+∠DAC； ∠DAE =∠EAC+∠DAC； ∠DAC=∠DAC

So ∠BAD=CAE means △BAD and △CAE congruence (SAS), so BD=CE.

3: AB+BD=DE

Prove: AD⊥BC,BD=DC, so △ABC is an isosceles triangle and AB=AC.

And c has CA=CEF on the vertical line of AE, so AB=AC=CE.

So AB+BD=CE+DC=DE

4. Because AB = CD and AD = BC, the quadrilateral ABCD is a parallelogram and AD is parallel to BC.

So: ∠ 1=∠2 internal dislocation angles are equal.