Question

in parallelogram ABCD, bisectors of consecutive angle A And Angle B intersect at a point P. prove that angle APB=90degree.​

Answer 1

Answer:

in parallelogram abcd,

a+b=180(consecutive angles)

angle DAP + angle PAB=a (AP bisects a)

angle PBC + angle PBA=b (PB bisects b)

PAB=1÷2×a

PBA=1÷2×b

1÷2×a+1÷2×b=1÷2×180

PAB+PBA=90 - (1

in triangle pab,

PAB+PBA+APB=180(a.s.p. of triangle)

from 1)

90+APB=180

⇒APB=90

Step-by-step explanation:

Answer 2

Refer The Attachment ⬆️

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