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Answer :

Answer:

  • x = 4
  • ∠DEG = 32°

Step-by-step explanation:

We know that:

  • If a rectangle is divided by its diagonals, it will form 4 isosceles triangles (ΔDGH, ΔFHE, ΔGHF, ΔDHE).
  • ΔFHE = 180 = 64 + 2y
  • ΔGHF = Isosceles triangle [∠G = ∠F]

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  • 180 = 64 + 2(FEH)
  • => 116 = 2(FEH)
  • => ∠FEH = 116/2 = 58

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  • => 90 - 58 = ∠DEG
  • => ∠DEG = 32°

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  • => 90° = 6x + 8 + 58
  • => 90° = 6x + 66
  • => 90 - 66 = 6x
  • => 24 = 6x
  • => x = 4

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