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]
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