In a circle with centre O, BC is a chord. Point D and A are on the circle, on the opposite side of BC, such that ∠DBC = 28° and BD = DC. What is the measure of ∠BOC?

Answer: Option C

∠DBC = 28°   (Given)
BD = DC,   (Given)
∠BCD = 28°
So, ∠BDC = 180° - (28° + 28°) = 124°
∠BAC = 180° - 124° = 56°
(Cyclic $$\square$$)
∠BOC = 2 × ∠BAC = 56° × 2 = 112° Answer.