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]

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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