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ABCD is a rhombus with (angle …

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ABCD is a rhombus with (angle ABC= 40•) . Find the measure of angle ACD .
  • 2 answers

Abhishek Chauvhan 3 years, 10 months ago

ABC is Currently

Yogita Ingle 3 years, 10 months ago

Given ABCD is a rhombus.
Diagonals bisect each other perpendicularly. 
Hence ∠BOC = 90°
Given ∠OCB = 40°  
AD||BC and BD is the transversal
∴ ∠ADB = ∠DBC (Alternate angles)
 Hence in right angled DBOC,
 ∠BOC + ∠OCB + ∠OBC = 180° 
⇒ 90° + 40° + ∠OBC = 180° 
⇒130° + ∠OBC = 180° 
⇒ ∠OBC = 180° - 130° = 50° 
But ∠OBC = ∠DBC 
Therefore, ∠ADB = 50°

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