Question

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Answer 1

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Answer 2

1) In quadrilateral ABCD, AB = BC = CA and CD = AD. If ∠B = 60° and ∠ACD = 68°. Find ∠BAD, ∠BCD and ∠D.

Answer -

Given :-

  AB = BC = CA

  ∠B = 60°

  CD = AD

  ∠ACD = 68°

Proof :-

  In Δ ABC

  AB = BC = CA (Given)

  ∠B = 60° (Given)

If the three side[ AB, BC and AD ] of the Δ ABC are equal, it means Δ ABC is an equilateral triangle..

So, ∠B[ ∠ABC ] = ∠BAC = ∠ACB (Angles of an equilateral triangle)

∴ ∠ABC = ∠BAC = ∠ACB = 60°

In Δ ACD

   CD = AD (Given )

  ∠ACD = 68° (Given )

  ∠DAC = ∠ACD = 68° ( Angles opposite to equal sides are equal... )

   ∠BAD = ∠BAC + ∠DAC

               = 60° + 68°

               = 128°

 ⇒   ∠BAD = 128°

  ∠BCD = ∠ACB + ∠ACD

              = 60° + 68°

              = 128°

⇒   ∠BCD = 128°

   ∠D = 180° - [ ∠ACD + ∠DAC ]

          = 180° - [ 68° + 68° ]

          = 180° - 136°

          = 44°  

 ⇒  ∠D = 41°

HOPE IT HELPS . . .