Question

In figure O is the centre of the circle if angle AOC=130° then find angle ABC?​

Answer 1

I am sure as it is 130 as it the quadrilateral which is inscribed in a circle is cyclic quadrilateral so in cyclic quadrilateral sum of two consecutive angle is 180...

therefore

angle abc = 180 ° - 130 °

= 50°

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Answer 2

Given:

• ∠AOC = 130°

To Find:

• The angle ABC.

Solution:

First, draw lines from points A and C towards the upper direction of the circle.

We know that the angle subtended by a chord on a major area is equal to half the angle subtended at the center.

∴ ∠ADC = 1/2(∠AOC)

Substitute the value of angle AOC from the given data in the above formula we get,

⇒ ∠ADC = 1/2×(130°) = 65°

We get a figure ADCB which is a cyclic quadrilateral which implies that the sum of the opposite angles will be equal to 180°

⇒ ∠ABC + ∠ADC = 180°

On substituting the value of angle ADC which was obtained from the previous calculation in the above equation we get,

⇒ ∠ABC + 65° = 180°

⇒ ∠ABC = 180°-65° = 115°

∴The value of ∠ABC = 115°