Question

In the adjoining quadrilateral ABCD ,AO and BO are the bisector of

Answer 1

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>>In a quadrilateral ABCD. AO and BO are b

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In a quadrilateral ABCD. AO and BO are bisectors of angle A and angle B respectively. Prove that ∠AOB=

2

1

{∠C+∠D}.

Medium

Solution

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ABCD is a quadrilateral

To prove : ∠AOB=

2

1

(∠C+∠D)

AO and BO is bisector of A and B

∠1=∠2∠3=∠4...(1)

∠A+∠B+∠C+∠D=360

(Angle sum property)

2

1

(∠A+∠B+∠C+∠D)=180...(2)

In △AOB

∠1+∠3+∠5=

2

1

(∠A+∠B+∠C+∠D)

∠1+∠3+∠5=∠1+∠3+

2

1

(∠C+∠D)

∠AOB=

2

1

(∠C+∠D)