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

Sum of angles of a quadrilateral is 360°

In the quadrilateral ABCD

∠A + ∠B + ∠C + ∠D = 360°

∠A + ∠B =

…….(i)

Now in Δ DOC

[Sum of angles of a triangle is 180°]

……….(ii)

From above equations (i) and (ii) RHS is equal therefore LHS will also be equal.

Therefore

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