In the figure (ii) given below, O is the center of the circle. Calculate the values of x and y.

From figure,

⇒ ∠AOB + Reflex ∠AOB = 360°
⇒ 120° + Reflex ∠AOB = 360°
⇒ Reflex ∠AOB = 360° - 120°
⇒ Reflex ∠AOB = 240°.

Arc AB subtends Reflex ∠AOB at center and ∠ADB at point D of circle.

⇒ Reflex ∠AOB = 2 ∠ADB
⇒ 2∠ADB = 240°
⇒ ∠ADB = $\dfrac{240°}{2}$
⇒ ∠ADB = 120°
⇒ y° = 120°

Arc AB subtends ∠AOB at center and ∠ACB at point C of circle.

⇒ ∠AOB = 2 ∠ACB
⇒ 2∠ACB = 120°
⇒ ∠ACB = $\dfrac{120°}{2}$
⇒ ∠ACB = 60°
⇒ x° = 60°

Hence, the value of x = 60 and y = 120.