Lines AB and CD are parallel, with AB above CD, A to the left of B and C to the left of D. A point E lies between the two lines, to the left of both B and D, and is joined to B and to D. If $\angle ABE = 40^\circ$ and $\angle CDE = 55^\circ$, what is $\angle BED$?

Explanation

1. 01

   Draw a line through E parallel to AB (and so to CD). It splits $\angle BED$ into two parts.

2. 02

   The upper part equals $\angle ABE = 40^\circ$ (alternate angles).

3. 03

   The lower part equals $\angle CDE = 55^\circ$ (alternate angles).

4. 04

   $\angle BED = 40^\circ + 55^\circ = 95^\circ$.