# In a quadrilateral ABCD, AO and BO are bisectors of angle A and angle B respectively meeting at O. Prove that angle AOB = half of [angle C+ angle D]

1 answer

###### Question:

In a quadrilateral ABCD, AO and BO are bisectors of angle A and angle B respectively

meeting at O. Prove that

angle AOB = half of [angle C+ angle D]

meeting at O. Prove that

angle AOB = half of [angle C+ angle D]

## Answers

Answer: ABCD is a quadrilateralTo prove : ∠AOB= 21 (∠C+∠D)AO and BO is bisector of A and B ∠1=∠2∠3=∠4...(1)∠A+∠B+∠C+∠D=360(Angle sum property)21 (∠A+∠B+∠C+∠D)=180...(2)In △AOB∠1+∠3+∠5= 21 (∠A+∠B+∠C+∠D)∠1+∠3+∠5=∠1+∠3+ 21 (∠C+∠D)∠AOB= 21 (∠C+∠D) Explanation: In a quadrilateral ABCD. AO and BO are bisectors of angle A and angle B respectively. Prove that ∠AOB= 21 {∠C+∠D}.

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