State if the given statement is true or false with reference to the given figure. “The pairs of adjacent angles are

∠DOA,∠DOC
,

∠BOC,∠COD
,

∠AOD,∠BOD
and

∠AOC,∠BOC

and the linear pairs of angles are

∠AOD,∠BOD
and

∠AOC,∠BOC

.”

Question

State if the given statement is true or false with reference to the given figure. “The pairs of adjacent angles are

∠DOA,∠DOC
   ,
    
     ∠BOC,∠COD
   ,
    
     ∠AOD,∠BOD
   and
    
     ∠AOC,∠BOC
   
   and the linear pairs of angles are

∠AOD,∠BOD
   and
    
     ∠AOC,∠BOC
   
  .”

Accepted Answer

It is given that “The pairs of adjacent angles are

∠DOA,∠DOC
   ,
    
     ∠BOC,∠COD
   ,
    
     ∠AOD,∠BOD
   and
    
     ∠AOC,∠BOC
   
   and the linear pairs of angles are

∠AOD,∠BOD
   and
    
     ∠AOC,∠BOC
   
  .” Let us observe the given figure.We know that adjacent angles are those which have a common vertex and a common arm.We can observe that the following are the pairs of adjacent angles in the given figure.

⇒∠DOA,∠DOC

⇒∠BOC,∠COD

⇒∠AOD,∠BOD

⇒∠AOC,∠BOC
  Similarly linear pair of angles are those which lie on a straight line and add up to give 180°. Hence, we can write that, the following pairs are linear angles.

⇒∠AOD,∠BOD

⇒∠AOC,∠BOC
  The pairs of adjacent angles are

∠DOA,∠DOC
   ,
    
     ∠BOC,∠COD
   ,
    
     ∠AOD,∠BOD
   and
    
     ∠AOC,∠BOC
   
   and the linear pairs of angles are

∠AOD,∠BOD
   and
    
     ∠AOC,∠BOC
   
  . Hence, the correct option is 1.

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State if the given statement is true or false with reference to the given figure. “The pairs of adjacent angles are ∠DOA,∠DOC , ∠BOC,∠COD , ∠AOD,∠BOD and ∠AOC,∠BOC and the linear pairs of angles are ∠AOD,∠BOD and ∠AOC,∠BOC .”

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