Question

The bisectors of any two adjacent angles of a parallelogram intersect at :

A. 30° 

B. 45° 

C. 60° 

D. 90°

Answer 1

Option : (D)

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° 

(Sum of interior angles on the same side of the transversal is 180°) 

∠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.