ABCD is a rhombus such that ∠ACB = 50°. Then find ∠ADB.
Question
ABCD is a rhombus such that ∠ACB = 50°. Then find ∠ADB.
Solution
In a rhombus, diagonals bisect each other at right angles and also bisect the angles of the rhombus.
Given that ∠ACB = 50°, we know that the diagonal AC bisects ∠A and ∠C of the rhombus.
Therefore, ∠BAC = ∠BCA = 50°.
Since the diagonals bisect each other at right angles, ∠BAD = 90° - ∠BAC = 90° - 50° = 40°.
But, ∠BAD is half of ∠ADB (since the diagonals bisect the angles of the rhombus).
Therefore, ∠ADB = 2 * ∠BAD = 2 * 40° = 80°.
So, ∠ADB = 80°.
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