Question

In a parallelogram abcd, bisectors of consecutive angles a and b intersect at p. prove that angle apb is equal to 90o.

Answer 1

hey friend here is your answer

it is given that ABCD is a parallelogram so
angle A + angle b is equal to 180 degree (adjacent angles )
now in triangle abp
angle abp + angle bap+ angle apb
=180 degree (angle sum property of a triangle)
so half of angle A + half of Angle B + angle APB
= 180 degree
so 90 degree + angle APB is equal to 180 degree
therefore angle APB is equal to 90 degree (hence proved )

Answer 2

hi bro here is the answer

Given in parallelogram ABCD AO and BO are bisectors of angle A and angle B respectively.

thus
APB =90°