In a parallelogram A B C D, A P and B P are the angle bisectors of \angleD A B and \angleA B C. Find \angleA P B

Management Aptitude Test Dec 2019 Paper

Question : 86 of 200

Marks: +1, -0

In a parallelogram

A B C D

A P

and

B P

are the angle bisectors of

∠D A B

and

∠A B C

. Find

∠A P B

$85°$
$90°$
$94°$
$86°$

Validate

Solution:

AP is the angle bisector of ∠DAB

⇒ ∠PAB =

1/2

∠DAB ....(i)
and BP is the angle bisector of ∠ABC
⇒ ∠PBA =

1/2

∠CAB ....(ii)
Now, in a parallelogram sum of adjacent angles is 180°.
∴ ∠DAB + ∠ABC = 180°
From Eqs. (i) and (ii),
2[∠PAB + ∠PBA] = 180°
⇒ ∠PAB + ∠PBA = 90°
In ΔPAB, ∠PAB + ∠PBA + ∠APB = 180°
⇒ We know, 90° + ∠APB = 180°
⇒ ∠ABP = 90°

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