ABCD is a cyclic quadrilateral. If ∠BCD=100∘ and ∠ABD=70∘, then find ∠ADB.
Given that ABCD is a cyclic quadilateral such that∠BCD=100∘ and ∠ABD=70∘.
Since opposite angles of a cyclic quadrilateral are supplementary,
∠DAB+∠DCB=180∘.
⟹∠DAB=180∘−∠DCB
=180∘−100∘=80∘
Consider △ADB, since sum of angles of a triangle is 180∘, we have
∠ADB+∠DAB+∠ABD=180∘
i.e.,∠ADB+80∘+70∘=180∘
⟹∠ADB=180∘−150∘=30∘