let center be O
then join OA and OB
Then OAB becomes an equilateral triangle
OBA=OAB=BOA=60

and since angle BOA and X lie on the same base and
BOA makes angle on center and x makes angle on the circumference
we can use the geometry theorem
So x will be half of BOA
i.e x=1/2 x 60 = 30

Let O be the center of the circle

Join OA and OB, This represents the equilateral triangle.

angle(OAB)=angle(OBA)=angle(AOB)=60

Join OY, FROM triangle AOY

angle(OAY)=angle(OYA)=10 (60-50)

now take triangle BOY, which is an isosceles triangle (OB=OY)

angle(OYB)=angle(OBY)=x+10

Hence for triangle ABY

50+60+x+10+x=180
=> 120+2x=180
=> 2x=60
=> [spoiler]x=30[/spoiler]