Question
In the given figure, ABCD and BDCE are parallelograms with common base DC. If BC⊥BD, then ∠BEC is equal to
a) 60∘
b) 30∘
c) 150∘
d) 120∘
In the given figure, ABCD and BDCE are parallelograms with common base DC. If BC⊥BD, then ∠BEC is equal to
a) 60∘
b) 30∘
c) 150∘
d) 120∘
Answer:
:
∠BAD=30∘ [given]
∴ ∠BCD=30∘ [∵ opposite angles of a parallelogram are equal]
In ΔCBD, by angle sum property of a traingle, we have,
∠DBC+∠BCD+∠CDB=180∘⇒90∘+30∘+∠CDB=180∘⇒∠CDB=180∘−120∘=60∘
∴∠BEC=∠CDB=60∘ [∵ opposite angles of a parallelogram are equal]
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:
∠BAD=30∘ [given]
∴ ∠BCD=30∘ [∵ opposite angles of a parallelogram are equal]
In ΔCBD, by angle sum property of a traingle, we have,
∠DBC+∠BCD+∠CDB=180∘⇒90∘+30∘+∠CDB=180∘⇒∠CDB=180∘−120∘=60∘
∴∠BEC=∠CDB=60∘ [∵ opposite angles of a parallelogram are equal]
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