Solution: Because ∠ BDC = ∠ A+∠ Abd = 60 (one outer angle of a triangle is equal to the sum of two non-adjacent inner angles).

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.