Question

Q.6 In adjoining figure; angle BAO = 50° and angle BCO=20°, reflex angle AOC
(A) 140
(B) 220
(C) 120°
(D) 240​

Answer 1

Given : o is the centre of the circle angle aoc =100°

To Find : measures of angle abc and angle adc

Solution:

O is the centre of the circle

∠AOC = 100°

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

=> 100° =  2∠ABC

=>∠ABC  = 50°

ABCD is a cyclic quadrilateral

Sum of opposite angles of cylic quadrilateral = 180°

=> ∠ABC + ∠ADC= 180°

=>50° + ∠ADC = 180°

=> ∠ADC = 130°

∠ABC  = 50°

∠ADC = 130°

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