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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 .

Posted by Anuj Kumar 5 years, 2 months ago

CBSE > Class 09 > Mathematics

2 answers

Abhishek Chauvhan 5 years, 2 months ago

ABC is Currently

0Thank You

Yogita Ingle 5 years, 2 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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