In the given figure, `ABCD` is a cyclic quadrilateral in which `/_ A = (2x+4)^(@), /_ B = (x+10)^(@) , /_ C = (4y -4)^(@)` and `/_ D = (5y+ 5)^(@)` .Find the values of `x` and `y` . Hence, find the measure of each angle.

Explanation

We know that the opposite angles of a cyclic quadrilateral are supplementary.
`:. /_ A+ /_ C = 180^(@) ` and `/_ B + /_ D = 180^(@)`
`implies ( 2x+4) + (4y-4) = 180` and `(x+10) + (5y+5) = 180`
`implies 2x+4y = 180` and `x+5y = 165 `
`implies x+2y= 90` .....(i) and `x+5y = 165 ` ....(ii)
On solving (i) and (ii) , we get `x= 40` and `y=25`
`:. /_ A = (2 xx 40 +4)^(@) = 84^(@) , /_B = ( 40^(@) +10^(@)) = 50^(@)`
`/_ C = ( 4xx 25 -4) = 96^(@)` and `/_ D = (5 xx 25 +5)^(@) = 130^(@)`