Question

in fig de//qr and ap and bp are bisector of angles EAB and RBA. Find angle APB

Answer 1

see diagram enclosed
Let angle EAP = angle BAP = x    (AP bisector)Let angle RBP = angle PBA = y    BP is bisector
angle EAB + angle ABR = 180 degrees  as AE and BR are parallel
2 * x + 2 * y = 180 deg        x + y = 90
angle APB = 180 - x - y  in trianle APBangle APB = 180 - 90 = 90 deg