in a quadrilateral, CO and DO are the bisectors of angle C and angle D respectively. Prove that angle A +angle B=2angleCOD.
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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)
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)
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