Question

'O' is the center of a circle and angle AOC=150degrees, find angle ABC. ​

Answer 1

Answer :

Given :

<AOC = 150

To find : <ABC ..

Solution :

   If < AOC = 150 , then <ADC = $\frac{1}{2}$ <AOC { angles subtended at the centre of the circle by an arc is double the angle subtended anywhere else on the circle by the same arc } .

So , <ADC = 75 degrees ..

 Now we can see that ABCD is a cyclic quadrilateral and in a cyclic quadrilateral opposite angles are SUPPLEMENTARY .

   Hence , <ADC + <ABC = 180

               75 + <ABC = 180

                 <ABC = 180 - 75 =  105 degrees ...

Therefore <ABC = 105