Question

In the circle with centre O. AB = BC = CD and angle AOB = 40°
Calculate angle AOD angle AED angle BED​

Answer 1

Given : circle with centre O

AB = BC = CD = DE  and angle AOB = 40°

To Find : ∠AOD ,   ∠AED ,  ∠BED​

Solution:

AB = BC = CD = DE  

=>  ∠AOB =  ∠BOC =  ∠COD =  ∠DOE

∠AOB = 40°

=> ∠AOB =  ∠BOC =  ∠COD =  ∠DOE = 40°

∠AOD = ∠AOB +  ∠BOC +  ∠COD

=> ∠AOD =  40° +   40° +   40°

=>  ∠AOD =  120°

∠AED = (1/2)∠AOD

=> ∠AED = (1/2) 120°

=> ∠AED = 60°

∠BOD = ∠BOC +  ∠COD

=> ∠BOD =    40° +   40°

=>  ∠BOD =  80°

∠BED = (1/2)∠BOD

=> ∠BED = (1/2)80°

=> ∠BED = 40°

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