I’m going to make use of a theorem called Ceva’s Sine theorem, which states that, in the below figure, the product of the sines of angles a, c and e is equal to the product of the sines of angles b, d and f.

In our question, a and d are unknown, and b, c, e and f are 6, 24, 12 and 54 respectively.

sin(a).sin(24).sin(12) = sin(6).sin(d).sin(54)

(sin(24).sin(12))/( sin(6).sin(54)) = sin(d)/sin(a)

sin(d)/sin(a) = 1

sin(d) = sin(a)

But since the six angles must total 180 degrees, a + d = 84, therefore a = d = 42.

So our unknown angle x is equal to 42 degrees.