Question

In a quadrilateral ABCD, CO and DO are the bisectors of ∠C and ∠D respectively. Prove that ∠COD = 1/2 (∠ + ∠B).

Answer 1

Angle COD= 180°- 1/2angle C-1/2 angle D=180°-1/2(angle C+D) ------- 1
Angle (A+B+C+D)=360°
AngleC+D= 360 - AngleA- angle B ----------- (2)
Substituting (2) in (1)
Angle COD= 180°-1/2(360°- angle A- Angle B)
Angle COD= 180 - 180 +1/2 Angle A + 1/2 Angle B= 1/2(Angle A+ Angle B)