Question

in the figure if o is the centre of the circle and angle AOC =140, find x

Answer 1

Answer:

The measure of ∠x=110°

Step-by-step explanation:

Given ∠AOC=140° in the figure  

we have to find the value of x

∠AOC of minor sector=140°

∠AOC of major sector=360°-140°=220°

By theorem the angle subtended at the centre is twice the angle formed at the circumference of circle.

Hence,

$\angle x=\frac{1}{2}(\angle AOC)=\frac{1}{2}\times 220^{\circ}=110^{\circ}$

∴ The measure of ∠x=110°

Answer 2

Given : o is the centre of the circle angle aoc =140°

To Find : measure  of angle abc

Solution:

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°

∠ABC = 110°

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