If the BF intersection CD extends to m, the angle BFD= angle BMD+ angle FDM.

According to the condition of bisector of two angles, angle BFD= 1/2 (angle Abe+angle CDE).

Extend the intersection AB of DE to n, and the known angle BED= angle BND+ angle ABE= angle NDM+ angle ABE=75 degrees is defined by the external angle.

Therefore, BFD angle = 1/2 angular bed =37.5 degrees.