In the adjacent figure O is the centre of the circle. If `angle OAB=30^(@), angle ABC=120^(@), angle BCO=y^(@) and angle COA=x^(@)`, then the find value sof x and y.

Explanation

Accroding to the given figure, ` angle AOC=x^(@), angle ABC=120^(@), angle OCB=y^(@), angle BAC=30^(@)`
Now, the central angle produced by the are AC= reflex ` angle AOC` angle in circle `= angle ABC=120^(@)`

`:.` reflex `angle AOC= 2 xx angleABC` [ by theorem-34] `=2xx120^(@)=240^(@)`
Then `angleCOA=360^(@)-` reflex `angleAOC=360^(@)-240^(@)=120^(@)`
`:. x^(@)=120^(@) rArr x=120`
Again, `angleAOC+angleOCB+angleOAB+angleABC=360^(@) [ :.` the sum of 4 angle of a quadrilaterl is `360^(@)`]
or , `120^(@)+y^(@)+30^(@) or, y^(@)=36^(@)-270^(@), or y^(@)=90^(@)`
`:. x=120 and y=90`