Math, asked by arnuv44, 1 year ago

in given figure o is centre of the circle if angle aoc =130 then find angle abc

please answer fast

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Answered by samiksha83
1

Here is your answer.....

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arnuv44: yhank you very much !!!
samiksha83: welcome
Answered by Anonymous
0

Join A and C to any point P in major arc AC.

We know that the angle subtended by an arc of a circle at the centre is double the angle subtended by it any point on the remaining part of the circle.

 \therefore \angle APC  =  \frac{1}{2} \angle  AOC  \\ =  >  \frac{1}{2} (130 \degree)  \\ = >  65 \degree

Now, ABCP is a cyclic quadrilateral and sum of opposite angles in a cyclic quadrilateral is 180°

 \therefore\angle APC  + \angle ABC = 180 \degree

 =  >  \angle ABC = 180 \degree -  \angle APC

 =  >   180 \degree - 65 \degree

 =  > 115 \degree

Therefore, \boxed{\angle ABC = 115\degree}

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