In the figure, AB is parallel to CD. If angle B = 30 degrees and angle D = 40 degrees, find angle BED.

Solution:

Draw a line through E parallel to AB and CD.

Let the line be FG, where F is on the left of E and G is on the right of E. So, FG || AB || CD.

Since FG || AB, and BE is a transversal, the alternate interior angles are equal.

Angle FEB = Angle B = 30 degrees.

Since FG || CD, and ED is a transversal, the alternate interior angles are equal.

Angle GED = Angle D = 40 degrees.

Angle BED is the sum of Angle FEB and Angle GED.

Angle BED = Angle FEB + Angle GED

Angle BED = 30 degrees + 40 degrees

Angle BED = 70 degrees.

Answer: Angle BED = 70 degrees.