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 right of both B and D, and is joined to B and to D. If $\angle ABE = 150^\circ$ and $\angle CDE = 140^\circ$, what is $\angle BED$ (the angle less than 180°)?

Explanation

1. 01

   Since E is to the right, $\angle ABE$ is measured from BA (pointing left) round to BE, so the angle between BE and the rightward part of AB is $180^\circ - 150^\circ = 30^\circ$.

2. 02

   Similarly at D, the angle between DE and the rightward part of CD is $180^\circ - 140^\circ = 40^\circ$.

3. 03

   Draw a line through E parallel to AB. By alternate angles, $\angle BED = 30^\circ + 40^\circ = 70^\circ$.

4. 04

   Equivalently, $\angle BED = 360^\circ - 150^\circ - 140^\circ = 70^\circ$.