Q10 of 35 Page 3

  A diagonal and a side of a rhombus are of equal length. Find the measure of the angles of the rhombus.  

Let ABCD be the rhombus. AB = BC = DC = DA   (sides of a rhombus are equal) But AB = BD (Given) ∴ AB = BC = CD = DA = BD Since in Δ ABD all the sides are equal. Δ ABD is an equilateral Δ . Similarly Δ BCD is also an equilateral.                
  ∠ A = ∠ ABD = ∠ ADB = ∠ DBC = ∠ C = ∠ CDB = 600     
∴ ∠ B = ∠ ABD + ∠ DDC = 600 + 600 = 1200 and ∠ D = ∠ ADB + ∠ CDB = 600 + 600 = 1200
∴ The angles of the rhombus are 600, 1200, 600 and 1200.

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