∫BD is the bisector of∠ ∠ABC ∴∠ABD=∠DBC.

∫∠DCF is the external angle of △BDC ∴∠DCF=∠DBC+∠D (the external angle of a triangle is equal to the sum of two non-adjacent internal angles), and acf is the external angle of △ABC.

∠∠ACF = 2∠DCF∠ABC = 2∠DBC ∴2∠dcf=2∠dbc+∠a

∴∠ A = 2 ∠ DCF-2 ∠ DBC and ∠D=∠DCF-∠DBC

∴∠A=2(∠DCF-∠DBC)=2∠D

∴∠A=2∠D