Math, asked by sharmahriday18, 3 months ago

In a quadrilateral ABCD. AO and BO are bisectors of angle A and angle B respectively. Prove that ∠AOB=
2
1

{∠C+∠D}.​

Answers

Answered by arsh273
5

Answer:

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)

Step-by-step explanation:

Hope this will help

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