in the figure o is the centre of the circle angle aoc =80°find the measures of angle abc and angle adc
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Given : o is the centre of the circle angle aoc =80°
To Find : measures of angle abc and angle adc
Solution:
O is the centre of the circle
∠AOC = 160°
∠AOC = 2∠ABC ( Angle formed by chord at center = twice angle formed in same arc segment)
=> 80° = 2∠ABC
=>∠ABC = 40°
ABCD is a cyclic quadrilateral
Sum of opposite angles of cylic quadrilateral = 180°
=> ∠ABC + ∠ADC= 180°
=>40° + ∠ADC = 180°
=> ∠ADC = 140°
∠ABC = 40°
∠ADC = 140°
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