Question

in the figure O, is the center of th circle such that measure of angle AOC=140 then find the measure of angle ABC​

Answer 1

ANSWER    ABC = 110°

EXPLANATION  

O is the centre of the circle

Take a point D in remaining arc

∠AOC = 140°

∠AOC = 2∠ADC ( Angle formed by chord at center = twice angle formed in same arc segment)

=> 140° =  2∠ADC

=>∠ADC  = 70°

ABCD will be  a cyclic quadrilateral

Sum of opposite angles of cylic quadrilateral = 180°

=> ∠ABC + ∠ADC= 180°

=>70° + ∠ABC = 180°

=> ∠ABC = 110°