∵AB//CD,∠B=40°,∴∠DFB=∠B=40°
∴∠CFB=140°,又∠CFE:∠EFB=3:4
∴EFB=140°÷7×4=80°
∴∠BEF=180°-∠B-∠EFB=180°-40°-80°=60°