Question

in parallelogram ABCD bisectors of two consecutive angles A and B intersect at P prove that angle APB=90

Answer 1

Here angle A + angle B = 180 (in a parallelogram consecutive angles are supplementary)

angle PAB =1/2angleA
angle PBA =1/2angle B

angle PAB + angle PBA = 1/2 ( angle A + angleB)
angle PBA + angle PAB = 1/2 × 180
angle PBA + angle PAB = 90 degree

In triangle PAB :-

angle PAB + angle PBA + angle APB = 180 degree. ( angle sum property of a triangle)

angle APB + 90 = 180

angle APB = 90 degrees

Hence it is proved

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Answer 2

Refer The Attachment ⬆️

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