Let, ABCD is a parallelogram

OA and OD are the bisectors of adjacent angles ∠A and ∠D

As, ABCD is a parallelogram

Therefore,

AB || DC (Opposite sides of the parallelogram are parallel)

AB || DC and AD is the transversal,

Therefore,

∠BAD + ∠CDA = 180^o (Sum of interior angles on the same side of the transversal is 180^o)

∠1 + ∠2 = 90° (AO and DO are angle bisectors ∠A and ∠D) (i)

In ΔAOD,

∠1 + ∠AOD + ∠2 = 180°

∠AOD + 90° = 180° [From (i)]

∠AOD = 180° – 90°

= 90°

Therefore,

In a parallelogram, the bisectors of the adjacent angles intersect at right angle.