Question

In the adjoining quadrilateral ABCD AO and BO are the bisectors of angle A and angle B respectively. Prove that angle AOB = 1/2 (angle C + angle B)

Answer 1

Step-by-step explanation:

Gn:

ABCD is a quadrilateral

AO and BO are bisectors of ∠A and ∠B respectively.

To prove:

∠AOB = 1/2 (∠C + ∠B)

Proof:

Let ∠A = A, ∠B = B, ∠C = C, ∠D = D

taking ABCD:

A + B + C + D = 360 (∠ sum property)

A + B = 360 - (C + D)

1/2 (A + B) = 1/2 (360 - (C + D))

1/2 (A + B) = 180 - 1/2 (C + D)

1/2 (A + B) - 180 = - 1/2 (C + D)

180 - 1/2 (A + B ) = 1/2 (C + D) [Multiplying -1 to the eq. ]

AOB = 1/2 (C + D)

[ as AOB is a triangle, so 1/2 (A + B) + AOB = 180 ]

Hence Proved!