Question

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

Answer 1

Answer is 115 degrees

Answer 2

$From \: the \: figure , \\</p><p>O \: is \: the \: Center \: of \: the \: circle$

$\angle {AOC} = 130\degree$

$i ) \angle {ADC} = \frac{1}{2} \times \angle {AOC}$

_________________

/* By Theorem */

The angle subtended by an arc at the centre is twice the angle subtended by it at any point on the remaining part of the circle .

___________________

$= \frac{1}{2} \times 130 \\=65 \degree$

$ABCD \: is \: Cyclic \: Quadrilateral.$

$\angle {ABC} + \angle {ADC} = 180\degree$

$\blue { ( Opposite \: angles \: in \: a \:}\\\blue {\: cyclic\: Quadrilateral\: Supplementary )}$

$\implies \angle {ABC} + 65 = 180$

$\implies \angle {ABC} = 180 - 65 \\= 115\degree$

Therefore.,

$\red { Value \:of \:\angle {ABC}} \green {=115\degree}$

•••♪