Question

In a quadrilateral AP and BP are angle inspectors of angle A and angle B find angle APM if angle c is 100 and angle D is 70​

Answer 1

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 APB

angle APB = 180 - 90 = 90 deg