Management Aptitude Test Dec 2019 Paper

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°