As shown in the figure, parallel lines Mn and PQ passing through O and E respectively are AB.

Then ∠ Abe =∠BEQ, ∠QED=∠CDE.

∠ABO=∠BON，∠NOD=∠CDO

And ∠BED=∠BEQ+∠QED, ∠BOD=∠BON+∠NOD.

Be and ed are bisectors of angle ABO and angle CDO,

∠BED =∠BEQ+∠QED = 1/2∠ABO+ 1/2∠CDO = 1/2∠BON+ 1/2∠NOD = 1/2∠BOD

Is that a bed? =? 1/2∠BOD