In a quadrilateral,COand Do are the bisectors of angle C and angle D respectively.prove that angle A+ angle B=2 angle COD
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let ABCD is a quadrilateral
CO and Do are the bisectors pf angle C and Angle D
To prove that angle A+angle B= 2angleCOD we get
in the quadrilateral ABCD
angleA+angleB +angleC = 360 (sum of angles of a quadrilateral) -1
in triangle DOC
angle COD + angleDCO + angleCDO= 180 ( sum of angles of aquadrilateral)----2
2COD+2DCO+2CDO=360(multiplying both sides with 2)
a2angleCOD = 360-- (2angleDCO--2angleCDO)
2COD = 360 -( angleC +angleD) ( CO and DO are the bisectors of angle C and angleD)
from 1 and 2 we get 2COD = angleA + angleB
therefore angle A + angle B = 2angleCOD
CO and Do are the bisectors pf angle C and Angle D
To prove that angle A+angle B= 2angleCOD we get
in the quadrilateral ABCD
angleA+angleB +angleC = 360 (sum of angles of a quadrilateral) -1
in triangle DOC
angle COD + angleDCO + angleCDO= 180 ( sum of angles of aquadrilateral)----2
2COD+2DCO+2CDO=360(multiplying both sides with 2)
a2angleCOD = 360-- (2angleDCO--2angleCDO)
2COD = 360 -( angleC +angleD) ( CO and DO are the bisectors of angle C and angleD)
from 1 and 2 we get 2COD = angleA + angleB
therefore angle A + angle B = 2angleCOD
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