Question
ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC=80∘ and ∠BAC=40∘, then find ∠BCD.
Answer: Option A
:
A
Given that ∠BAC=40∘and∠DBC=80∘.
Since the angles formed by the same segment are equal,
∠BDC=∠BAC=40∘.
InΔBDC,
∠BDC+∠DBC+∠BCD=180∘.[Angle sum property]
i.e., 40∘+80∘+∠BCD=180∘
⟹∠BCD=180∘−120∘=60∘
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:
A
Given that ∠BAC=40∘and∠DBC=80∘.
Since the angles formed by the same segment are equal,
∠BDC=∠BAC=40∘.
InΔBDC,
∠BDC+∠DBC+∠BCD=180∘.[Angle sum property]
i.e., 40∘+80∘+∠BCD=180∘
⟹∠BCD=180∘−120∘=60∘
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