(b) 150°
ΔAOB is equilateral
⇒ AO = OB = AB and
∠OAB = ∠OBA = ∠AOB = 60°
Also, ABCD being a square,
AB = BC = CD = AD
⇒ AO = AD and BO = BC
∠DAO = ∠CBO = 30° (∵ ∠OAB = ∠OBA = 60°)
In ΔADO, AO = AD ⇒ ∠ADO = ∠AOD
= \(\frac{1}{2}\) (180° – ∠DAO) = \(\frac{1}{2}\) (180° – 30°) = 75°
Similarly, ∠BOC = 75°.
∴ ∠DOC = 360° – (∠AOB + ∠AOD + ∠BOC) = 360° – (60° + 75° + 75°) = 360° – 210° = 150°
