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Question
In the given figure, ABCD and BDCE are parallelograms with common base DC. If BC ⊥ BD, then ∠BEC = ______.
Options
60°
30°
150°
120°
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Solution
In the given figure, ABCD and BDCE are parallelograms with common base DC. If BC ⊥ BD, then ∠BEC = 60°.
Explanation:
Given: ∠BAD = 30°
So, ∠BCD = 30° ...[Opposite angles of a parallelogram are equal]
Now, In triangle CBD:
∠DBC + ∠BCD + ∠CDB = 180° ...[Sum of all angles of a triangle is equal to 180°]
90° + 30° + ∠CDB = 180°
∠CDB = 180° – 90° – 30°
∠CDB = 180° – 120°
∠CDB = 60°
Therefore, ∠BEC = 60° ...[Opposite angles of a parallelogram are equal]
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