There are:

Figure 1, ∠ bed and ∠BFD are equal.

Reason: The perpendicular lines of AB and CB on both sides of angle ABC pass through point D, and there are vertical feet of M and N respectively.

It is not difficult to prove that RT△MDE≌RT△NDF,

Therefore, ∠BED=∠BFD is obtained.

Figure 2, ∠ Bed +∠ BFD = 180.

Reason: Draw an arc with point D as the center and point DF as the radius, intersect BC at point M and connect DM, then DF=DM=DE. ∠DFM=∠DMF。

So: ∠ BFD+∠ DFM = 180.

According to the conclusion of figure 1, ∠DMF=∠DEB.

So: ∠ bfd+∠ bed = 180.

So ∠BFD=∠BED or ∠ bfd+∠ bed = 180.