In the given figure, O is the centre 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 = $\dfrac{230^{\circ}}{2}$

⇒ ∠ABC = 115°.

Hence, the value of ∠ABC = 115°.