Q3 of 23 Page 181

In a quadrilateral ABCD, the bisector of ∠C and ∠D intersect at O.

Prove that



Given :- ABCD is a quadrilateral


∠ OCB= ∠ OCD=∠C/2 [OC is bisector of ∠ C]


∠ ODA= ∠ ODC=∠D/2 [OD is bisector of ∠ D]


Formula Used:- ∠ A+ ∠ B+∠ C+ ∠ D=360°


Solution :-


In Δ COD


∠ OCD+ ∠ COD +∠ ODC=180°


∠D/2 + ∠C/2 +∠ COD = 180°


(∠ D+∠ C)/2 + ∠ COD = 180°


If;


∠ A+ ∠ B+∠ C+ ∠ D=360°


∠ C+ ∠ D=360° -(∠ A+ ∠ B)


+ ∠ COD=180°


180° - + ∠ COD=180°


∠ COD=


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