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Question
In the triangle ABC, BC = CD and (∠ABC−∠BAC)=30∘. The measure of ∠ABD is :
In the triangle ABC, BC = CD and (∠ABC−∠BAC)=30∘. The measure of ∠ABD is :
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Solution
The correct option is C 15∘
∠ABD=∠ABC−∠DBC
=∠ABC−∠BDC
=∠ABC−(∠ABD+∠BAD)
∴2(∠ABD)=∠ABC−∠BAD=30∘
∴∠ABD=15∘
∵∠BAD=∠BAC
∠ABD=∠ABC−∠DBC
=∠ABC−∠BDC
=∠ABC−(∠ABD+∠BAD)
∴2(∠ABD)=∠ABC−∠BAD=30∘
∴∠ABD=15∘
∵∠BAD=∠BAC
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