And because: a = 45.
So: ∠ Abd = 15.
Because BD is the bisector of ∠ABC, ∠ Abd = ∠ DBC = 15.
Because of DE//BC, ∠ Abd = ∠ BDE = 15 (two straight lines are parallel with equal internal angles).
In the triangle BDE ∠ Abd+∠ BDE+∠ Bed = 180 (triangle interior angle sum theorem).
So: ∠ bed = 150.