In triangle ABC,

∠A=

50
°

and BC is produced to a point D. If the bisectors of

∠ABC
and

∠ACD
meet at E, then the measure of

∠E
is ____ °.

Question

In triangle ABC,

∠A=
    
     50
    °

and BC is produced to a point D. If the bisectors of

∠ABC
   and

∠ACD
   meet at E, then the measure of

∠E
   is ____ °.

Accepted Answer

In triangle ABC,

∠A=
    
     50
    °

and BC is produced to a point D. If the bisectors of

∠ABC
   and

∠ACD
   meet at E, then the measure of

∠E
   is 25 °.Given a triangle ABC in which

∠A=
    
     50
    °

and BC is produced to a point D and the bisectors of

∠ABC
   and

∠ACD
   meet at E.Exterior angle property states that if a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.Using exterior angle property in triangle ABC,

∠ACD = ∠A + ∠B ……. 
    1
   
   Dividing by 2,

⇒
    
     ∠ACD
    2
   
    = 
    
     ∠A
    2
   
    + 
    
     ∠B
    2
   
    ……. 
    2
   
   As,

⇒∠B = 2∠1 , ∠ACD = 2∠2
  Therefore,

⇒

2∠2 
     
    2
   
    = 
    
     ∠A
    2
   
    +

2∠1
     
    2

⇒∠2 = 
    
     ∠A
    2
   
    + ∠1 ………
    2
   
   Using exterior angle property in triangle BEC,

∠ECD = ∠1 + ∠E

⇒∠2 = ∠1 + ∠E ……….
      3

From equation 2 and 3,

⇒
      
       ∠A
      2
     
      + ∠1 = ∠1 + ∠E

⇒
      
       ∠A
      2
     
      = ∠E

⇒∠E = 
      
       ∠A
      2
     
      ……
      4

⇒∠E =
      1
      2
     
     × 50°

⇒∠E = 25°

Hence, the measure of

∠E
   is 25°.

In triangle ABC, $∠ A = 50 °$ and BC is produced to a point D. If the bisectors of $∠ A B C$ and $∠ A C D$ meet at E, then the measure of $∠ E$ is ____ °.

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In triangle ABC, ∠A= 50 ° and BC is produced to a point D. If the bisectors of ∠ABC and ∠ACD meet at E, then the measure of ∠E is ____ °.

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In triangle ABC, $∠ A = 50 °$ and BC is produced to a point D. If the bisectors of $∠ A B C$ and $∠ A C D$ meet at E, then the measure of $∠ E$ is ____ °.