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AO and DO are the bisector of angleA and angleD. Prove that angle AOD= 1/2 (angleB+angleC)

AO and DO are the bisector of angleA and angleD. Prove that angle AOD= 1/2 (angleB+angleC)

Grade:9

1 Answers

Vikas TU
14149 Points
6 years ago
The question is incomplete though i am assuming that ABCD is any quadilateral.
then
A +  B + C  + D = 180
write 
B + C = 180 – (A + D)
divide the whole eqn. by 2.
(B+C)/2 = 90 – (A+D)/2.........(1)
In triangle AOB also,
AOB = 180 – 0.5*(A+D).......(2)
Therefore from both the eqns.
AOD= 1/2 (angleB+angleC)
proved.
 

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