Math, asked by ms4888930, 5 months ago

In Fig. 20, OE is the bisector of angle BOD. If angle 1 = 70°, find the magnitudes of angles 2,3,4.​

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Answers

Answered by mohiddin2586
3

Answer:

Let ∠EOB=x

Given,  

∠EOB=∠EOD  [ ∵ OE is bisector of ∠BOD]  

         x=∠1.

=> ∠1=x=70  

o

.  

=> ∠BOD=∠1+x=(70+70)  

o

.

=>∠BOD=140  

o

.

According to the figure,

∠COB=∠AOD and

∠AOC=∠BOD=140  

o

   [ ∵ vertically opposite angles]      

       

We know that,  

sum of all the angles around a point =360  

o

 

∠BOD+∠AOD+∠AOC+∠COB=360  

o

 

∠BOD+∠AOD+∠BOD+∠AOD=360  

o

 

2∠BOD+2∠AOD=360  

o

 

∠BOD+∠AOD=180  

o

 

140+∠AOD=180  

o

 

∠AOD=180  

o

−140  

o

 

∠AOD=20  

o

 

=> ∠COB=20  

o

 

∠AOC=∠BOD=140  

o

   

∴∠2=∠4=20  

o

 and ∠3=140  

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