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.