Question

In a quadrilateral ABCD,the bisector of angle Cand angle D intersect at O.prove that angle COD=1÷2(angleA+angleB)

Answer 1

Angle COD= 1800- 1/2angle C-1/2 angle D=1800-1/2(angle C+D)----------(1)

Angle (A+B+C+D)=3600

AngleC+D= 3600 - AngleA- angle B--------------(2)



Substituting (2) in (1)

Angle COD= 1800-1/2(3600- angle A- Angle B)

Angle COD= 1800-1800+1/2 Angle A + 1/2 Angle B= 1/2(Angle A+ Angle B)