解:连接AD、DF、DB.∵六边形ABCDEF是正六边形,∴∠ABC=∠BAF=∠AFE,AB=AF,∠E=∠C=120°,EF=DE=BC=CD,∴∠EFD=∠EDF=∠CBD=∠BDC=30°,∵∠AFE=∠ABC=120°,∴∠AFD=∠ABD=90°,在Rt△ABD和RtAFD中AF=ABAD=AD∴Rt△ABD≌Rt△AFD(HL),∴∠BAD=∠FAD=12×120°=60°...