Question

O is the centre of the circle. Find the value of x.

R S Aggarwal Maths Class 9 (2018) Pg 445

Answer 1

In a cyclic qyadrilateral sum of opposite angle are 180
130+x=180
x = 50.
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Answer 2

It can be Solved by two ways:-
First Method :-
=> 130° + /_AOC = 360° [Complete Angle].
=> /_AOC = 360°-130°
=> /_AOC = 230°

=> x = 1/2 /_AOC [Angle on circumference is half on the angle on centre].
=> x = 1/2 x 230°
=> x = 115°

Second Method :-
Construction :- Produce A and C to a common point P.
Now,
/_APC = 1/2 x 130° [Angle on circumference is half of the angle of Centre ].
=> /_APC = 65°
Again,

=> /_APC+ x = 180° [opposite angles of Cyclic quadrilateral ].
=> 65° + x = 180°
=> x = 180°-65°
=> x = 115°

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