State whether the following statement is true or false.In the figure given below, if O is the point of intersection of two lines AB and CD such that

∠AOC+∠BOE=

70
°

and

∠BOD=

40
°

,
and then the measure of

∠BOE=

30
°

then the measure of and reflex

∠COE=

250
°

.
and reflex

Question

State whether the following statement is true or false.In the figure given below, if O is the point of intersection of two lines AB and CD such that

∠AOC+∠BOE=
    
     70
    °

and

∠BOD=
    
     40
    °
   
   ,
  and  then the measure of

∠BOE=
    
     30
    °

then the measure of  and reflex

∠COE=
    
     250
    °
   
   .
  and reflex

Accepted Answer

It is given that O is the point of intersection of two lines AB and CD such that

∠AOC+∠BOE=
    
     70
    °

and

∠BOD=
    
     40
    °
   
   .
 Using the vertically opposite angles property, we have,

∠BOD=∠AOC

⇒∠AOC=
      40
      °

It is given that,

∠AOC+∠BOE=
    
     70
    °
   
   .

⇒
    
     40
    °
   
   +∠BOE=
    
     70
    °

⇒∠BOE=
    
     30
    °

Using the linear pair property, we have,

∠AOC+∠BOC=
    
     180
    °

⇒∠AOC+∠COE+∠BOE=
    
     180
    °

⇒∠COE=
      180
      °
     
     −
      30
      °
     
     −
      40
      °

⇒∠COE=
      110
      °

Thus, the reflex of

∠COE
  is,

∠COE=
    
     360
    °
   
   −
    
     110
    °

⇒∠COE=
    
     250
    °

Therefore, if O is the point of intersection of two lines AB and CD such that

∠AOC+∠BOE=
    
     70
    °

and

∠BOD=
    
     40
    °
   
   ,
  then the measure of

∠BOE=
    
     30
    °

and reflex

∠COE=
    
     250
    °
   
   .
 Thus, the given statement is true.Hence, option (1) is correct.

Detailed Solution