Q. . In a quadrilateral ABCD, AO and BO are the bisectors of ∠ A and ∠ B respectively. Prove that AOB = 1/2( ∠ C + ∠ D) . Share with your friends Share 1 Neha Sethi answered this Dear student To prove: ∠AOB=12∠C+∠DGiven: AO and BO are the bisectors of ∠A and ∠B respectively.⇒∠1=∠4 and ∠3=∠5 ...1Proof: In quadrilateral ABCD, by angle sum property of quadrilateral∠A+∠B+∠C+∠D=360°12∠A+∠B+∠C+∠D=180° ...2Now in △AOB, by angle sum property of △∠1+∠2+∠3=180° ...3Equating 2 and 3, we get⇒12∠A+∠B+∠C+∠D=∠1+∠2+∠3⇒12∠A+12∠B+12∠C+∠D=∠1+∠2+∠3⇒∠1+∠3+12∠C+∠D=∠1+∠2+∠3 ∵12∠A=∠1 and 12∠B=∠3⇒12∠C+∠D=∠2⇒12∠C+∠D=∠AOBHence proved Regards 0 View Full Answer Akshat Mittal answered this Yg -1 Jatin Bansal answered this In ∆ AOB , √AOB+√OAB+, -2
