Question

there is a parallelogram ABCD.the bisectors of angle A and angle B of parellelogram ABCD meet at O. find the measure of angle AOB.

Answer 1

parallelogram ABCD

AO and BO are angles bisector of A and B.

We know that adjacent angles sum in a parallelogram is 180

2x+2y=180

x+y=90

⇒90+∠AOB=180

∴∠AOB=90

∘

Answer 2

Given :  In a parallelogram ABCD, the bisectors of ∠A and∠ B meet at O.

To Find : ∠AOB.

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Solution:

 In a parallelogram sum of adjacent angles is 180°

Hence ∠A + ∠B = 180°

the bisectors of ∠A and∠ B meet at O.

=> ∠OAB = ∠A/2   ∠OBA = ∠B/2

∠OAB + ∠OBA = ∠A/2 + ∠B/2

=> ∠OAB + ∠OBA = (∠A + ∠B)/2

=> ∠OAB + ∠OBA = (180°)/2

=> ∠OAB + ∠OBA = 90°

in  ΔOAB using triangle angle sun theorem:

∠OAB + ∠OBA  + ∠AOB =  180°

=> 90°  + ∠AOB =  180°

=> ∠AOB = 90°

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