The reason for this is the following：

∫DE∨AC，DF∨AB

∴∠ 1=∠fad,∠2=∠bac；

And AD is the angular bisector of △ABC.

∴∠DAE=∠DAF=？ ∠BAC

∴∠ 1=∠DAF=？ ∠BAC

∴∠2=∠BAC=2∠ 1

That is ∠ 2 = 2 ∠ 1.