Question

In a quadrilateral,COand Do are the bisectors of angle C and angle D respectively.prove that angle A+ angle B=2 angle COD​

Answer 1

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