Question

the angles of cyclic quadrilateral abcd are 6x+10,5x,x+y,3y-10 find x and y and hence the value of four angles

Answer 1

In quadrilateral ABCD
∠A = 6x+10 ,  ∠B = 5x     ,   ∠C = x+y      ,        ∠D = 3y-10

now for cyclic quadrilateral , sum of opposite angles equals 180.

∠A +∠C =180   ⇒   6x+10+x+y = 180
                         ⇒ 7x+y = 170          .........(1)

and ∠B + ∠D  = 180  ⇒  5x+3y-10 = 180
                             ⇒   5x +3y = 190            ..........(2)

solving  (1) and (2) gives x = 20      and y = 30

hope this helps.