Question

In the adjoining figure, ABCD is parallelogram, AE and BE are angle bisectors of ∠A and ∠B respectively. Show that ∠AEB=90°.

Answer 1

AE bisects angle A 

let each bisected angle be x 
angle A = 2x 

Similarly let y be each of the bisected angle

2y = angle B 

2x+2y = 180 deg ( adjacent angles of a parallelogram) 

x+y = 90 

In triangle ABE ,

x +y + angle AEB = 180 deg. ( sum of angles of a triangle) 
90°+angle AEB = 180°

Angle AEB = 180°-90°

Angle AEB = 90°

Answer 2

Answer:

AEB = 90°

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