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Question
ABCD is a rhombus such that ∠ACB = 40º. Then ∠ADB is ______.
Options
40º
45º
50º
60º
Solution
ABCD is a rhombus such that ∠ACB = 40º. Then ∠ADB is 50º.
Explanation:
Given, ABCD is a rhombus such that ∠ACB = 40º ⇒ ∠OCB = 40º
Since, AD || BC
∠DAC = ∠BCA = 40º ...[Alternate interior angles]
Also, ∠AOD = 90º ...[Diagonals of a rhombus are perpendicular to each other]
We know that, sum of all angles of a triangle ADO is 180º
∴ ∠ADO + ∠DOA + ∠OAD = 180º
∴ ∠ADO = 180º – (40º + 90º)
= 180º – 130º
= 50º
⇒ ∠ADB = 50º
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