It is known that AD is the bisector of ∠BAC and df⊥ac. de⊥ae.

Therefore, DE=DF, ∠ deb = ∠ DFC = 90.

It is also known that BD=CD

Therefore, Rt△DEB≌Rt△DFC(HL)

So ∠1= ∠ C.

It is known that ∠ 1+∠ 2 = 180.

So ∠ 1+∠ C = 180.

That is ∠ Abd+∠ C = 180.