Question

In the figure,O is the centre of the circle.angle AOB=100° find angle ADB

Answer 1

angle AOB=100
angle ACB=50 (angle made at centre is double the angle made at any other point)

now,ACBD is a cyclic quadrilateral , so angle ADB + angle ACB=180 ( sum of opposite angles of a cyclic quad. is 180)

therefore,angle ADB=180-50=130

ANSWER IS 130°

hope it helped.

Answer 2

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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