Question

In the given figure , O is the centre of circle such that angle AOC =130° then ABC=?

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Answer 1

Answer:

115°

Step-by-step explanation:

Reflex ∠AOC = 360 - 130

= 230° [Angles around a point add up to 360°)

∠ABC = 1/2 of Reflex ∠AOC [Angle at centre is twice angle at circumference]

∴ ∠ABC = 1/2*230°

∴ ∠ABC = 115°

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Answer 2

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