In the given figure, equilateral △ABC is inscribed in a circle and ABCD is a quadrilateral, as shown. Then ∠BDC = ?
(a) 90∘
(b) 60∘
(c) 120∘
(d) 150∘
ANSWER:
( c ) 120°
Since ΔABC is an equilateral triangle, each of its angle is 60°.
∴ ∠BAC = 60°
In a cyclic quadrilateral ABCD, we have:
∠BAC + ∠BDC = 180°
⇒ 60° + ∠BDC = 180°
⇒ ∠BDC = (180° - 60°) = 120°