Angles (Parallelogram and Triangle)

In the figure below, not drawn to scale, ABCD is a parallelogram, DE and AE are straight lines. Find the ∠AED.

Label the point with a 90 angle as F.

Method 1
CFE = 90 (adjacent angles on straight line BFC)
BCE = 65 (corresponding angles)
AED = 180 - 90- 65 = 25 (angle sum of triangle CFE)

Method 2
AFB = 90 (adjacent angles on straight line BFC)
ABC = 65 (diagonally opposite angles of parallelogram ABCD)
AED = BAF = 180 - 90 - 65 = 25 (angle sum of triangle BAF, alternate angles)