In the given figure, O is the centre of the circle and ∠AOC = 140^o. Find ∠ABC.

110^o

Calculation

O is the centre of the circle.

take a point D in remaining arc

∠AOC = 140^o

∠AOC = 2∠ADC (Angle formed by chord at centre = twice angled frame in same arc segment)

⇒ 140^o = 2∠ADC

⇒ ∠ADC = 70^o

ABCD will be a cyclic quadrilateral

Sum of opposite angles of cyclic quadrilateral = 180^o

⇒ ∠ABC + ∠ADC = 180^o

⇒ 70^o + ∠ABC = 180^o

⇒ ∠ABC = 110^o

Therefore, ∠ABC is 110^o