Draw the figure acc. to question to understand my solution.
Since diagonals are equal in length and bisect each other . You will get 4 isosceles triangle incide the reactangle.
AOB =120 => BOC = 180-120 = 60
Now since triangle AOB is isosceles
=> 2y = 180-120 = 60 => y = 30 .
Since traingle BOC is isosceles.
=> 2x = 180 - 60 = 120 => x =60