In the below figure, if

AB||CD,EF||BC,∠BAC=

65
°

and

∠DHF=

35
°

, the measure of

∠AGH
is ____ °.

Question

In the below figure, if

AB||CD,EF||BC,∠BAC=
    
     65
    °

and

∠DHF=
    
     35
    °

, the measure of

∠AGH
  is ____ °.

Accepted Answer

In the below figure, if

AB||CD,EF||BC,∠BAC=
    
     65
    °

and

∠DHF=
    
     35
    °

, the measure of

∠AGH
  is 100 °.Given a figure in which

AB||CD,EF||BC,∠BAC=
    
     65
    °

and

∠DHF=
    
     35
    °

.As we know that, vertically opposite angles are equal.Therefore,

∠DHF=∠GHC

⇒∠GHC=
        
         35
        °

As we know that, alternate interior angles are equal.

∠BAC=∠ACD

⇒∠ACD=
      65
      °

⇒∠GCH=
      65
      °

Using angle sum property in triangle GHC,

∠GCH+∠GHC+∠CGH=
        
         180
        °

⇒
        
         65
        °
       
       +
        
         35
        °
       
       +∠CGH=
        
         180
        °

⇒
        
         100
        °
       
       +∠CGH=
        
         180
        °

⇒∠CGH=
        
         180
        °
       
       −
        
         100
        °

⇒∠CGH=
        
         80
        °

Linear pair property states that the sum of angles of a linear pair is always equal to 180°. Using Linear pair property,

∠CGH+∠AGH=
        
         180
        °

⇒
        
         80
        °
       
       +∠AGH=
        
         180
        °

⇒∠AGH=
        
         180
        °
       
       −
        
         80
        °

⇒∠AGH=
        
         100
        °

Hence, the measure of

∠AGH is 100°
  .

In the below figure, if $A B | | C D, E F | | B C, ∠ B A C = 65 °$ and $∠ D H F = 35 °$ , the measure of $∠ A G H$ is ____ °.

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In the below figure, if AB||CD,EF||BC,∠BAC= 65 ° and ∠DHF= 35 ° , the measure of ∠AGH is ____ °.

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In the below figure, if $A B | | C D, E F | | B C, ∠ B A C = 65 °$ and $∠ D H F = 35 °$ , the measure of $∠ A G H$ is ____ °.