Let CD and EF intersect at point M, CF and BE intersect at point N, and let ∠ DEF = ∠ BEF = ∠ 1, ∠ DCF = ∠ BCF = ∠ 2.

Then in triangle EDM and triangle CFM, ∠EMD and ∠CMF are antipodal angles, then ∠ D+∠1= ∠ 2+∠ F.

Similarly, in triangle EFN and triangle BCN, substituting ∠ 1+∠F=∠B+∠2 into the data, the above two formulas can be subtracted to get ∠ F = 55.