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In the adjoining fig, AD = BC and ∠BAD = ∠ABC. If ∠BAD = 120 and ∠ABD = 35, then ∠CAD is
  • a)
    145
  • b)
    95
  • c)
    35
  • d)
    85
Correct answer is option 'D'. Can you explain this answer?
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In the adjoining fig, AD = BC and∠BAD =∠ABC. If ∠BAD= 120a...
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In the adjoining fig, AD = BC and∠BAD =∠ABC. If ∠BAD= 120a...
In the above diagram, It is given as:
AD=BC; Angle CBA=Angle DAB
So we can find angle CAD as follows:
     In Triangle BAD     Triangle BAC
                 BA                            BA     [Common line for the two triangles]
                 AD                            BC     [Given]
      Angle CBA                  Angle DAB     [Given]
               By RHS congruency, we can prove that Triangle BAD is congruent to Triangle BAC.
    So,
   Angle BAD=Angle BAC + Angle CAD
   =>Angle ABD=Angle BAC 
=> Angle BAC = 35 
Substituting,
120 = 35 +  Angle CAD
=>Angle CAD = 120 - 35
Angle CAD = 85.
Hence, explained.

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In the adjoining fig, AD = BC and∠BAD =∠ABC. If ∠BAD= 120and∠ABD= 35, then∠CADisa)145b)95c)35d)85Correct answer is option 'D'. Can you explain this answer?
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