Question

In a quadrilateral, CO and DO are the bisectors of Angle C and Angle D respectively. Prove that Angle A+ Angle B= 2 Angle COD.

Answer 1

Step-by-step explanation:

Given, AO and BO are the bisectors of angle A and angle B respectively.

∴ ∠1 = ∠4 and ∠3 = ∠5 ... (1)

To prove: ∠2 =(∠C + ∠D)

Diagram is on the top refer it.

Proof:

In quadrilateral ABCD

∠A + ∠B + ∠C + ∠D = 360°

(∠A + ∠B + ∠C + ∠D) = 180° ... (2)

Now in ΔAOB

∠1 + ∠2 + ∠3 = 180° ... (3)

equating (2) and (3), we get

∠1 + ∠2 + ∠3 =∠A +∠B +(∠C + ∠D)

∠1 + ∠2 + ∠3 = ∠1 + ∠3 +(∠C + ∠D)

∴ ∠2 =[∠C + ∠D]

Hence proved