The correct option is D L and M are not parallel.
Given, EO and FO are the angle bisectors and ∠BEO = 40° and ∠DFO= 55°.
Then, ∠FEO=∠BEO = 40°.
∠EFO=∠DFO = 55°.
We can write,
∠BEF=∠BEO+∠OEF
=40°+40°=80°
∠DFE=∠DFO+∠OFE
=55°+55°=110°
∠BEF+∠DFE=110°+80°=190°.
Hence, ∠BEF and ∠DFE doesn't form co- interior angles.
Then, L and M are not parallel.