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Question
In a rhombus ABCD, if ∠ACB = 40°, then ∠ADB =
Options
70°
45°
50°
60°
Solution
Rhombus ABCD is given as follows:
It is given that∠ACB = 40°.
Therefore, ∠OCB = 40° (Because O lies on AC)
We know that the diagonals of a rhombus intersect at right angle.
Therefore, ∠BOC = 90°
By angle sum property of a triangle, we get:
∠CBO + ∠OCB + ∠BOC = 180°
∠CBO + 40° + 90° = 180°
∠CBO+ 130° = 180 °
∠CBO = 50°
Since, O lies on BD
∠CBD = 50°
Also , CB || DA
Therefore,
∠ADB = ∠CBD
∠ADB = 50°
Hence, the correct choice is (c).
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