In the figure, given below, AD = BC,
∠ BAC=30∘ and
∠CBD=70∘. Find ∠ BCD
80∘
In the figure, ABCD is a cyclic quadrilateral AC and BD are its diagonals ∠ BAC=30∘ and ∠ CBD=70∘
∠ CAD=∠ CBD=70∘
Similarly ∠ BAC=∠ BDC=30∘
∴ ∠ BAD=∠ BAC+∠ CAD=30∘+70∘=100∘
Now ∠ BCD+∠ BAD=180∘
(opposite angles of cyclic quad.)
⇒ ∠ BCD+100∘=180∘
⇒ ∠ BCD=180∘−100∘=80∘