In the figure (ii) given below, it is given that O is the center of the circle and ∠AOC = 130°. Find ∠ABC.

From figure,

⇒ ∠AOC + Reflex ∠AOC = 360°
⇒ 130° + Reflex ∠AOC = 360°
⇒ Reflex ∠AOC = 360° - 130°
⇒ Reflex ∠AOC = 230°.

Arc AC subtends Reflex ∠AOC at center and ∠ABC at another point of circle.

⇒ Reflex ∠AOC = 2 ∠ABC

⇒ 2∠ABC = 230°

⇒ ∠ABC = $\dfrac{230°}{2}$

⇒ ∠ABC = 115°.

Hence, the value of ∠ABC = 115°.