In a quadrilateral ABCD, CO and DO are the bisectors of ∠ C and ∠ D respectively. Prove that ∠ COD = ( ∠ A+ ∠ B).

Question

In a quadrilateral ABCD, CO and DO are the bisectors of &#x2220; C and &#x2220; D respectively. Prove that &#x2220; COD = ( &#x2220; A+ &#x2220; B).

Philoid · Accepted Answer

Given,

In quadrilateral ABCD,

CO is the bisector of ∠C

DO is the bisector of ∠D

In ΔCOD

⇒ ∠COD =

⇒ ∠D+∠C = 360 – (∠A+∠B)

SO,

⇒ ∠COD =

⇒ ∠COD = (∠A+∠B) Proved.