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Simple solution
Suppose the length of AB = 1 unit
Because Angle ADB = Angle ABD = 50, so AD= 1 unit
Angle AEB =40
According to Sine law: AE/sin80 = AB/sin40= 1 unit /sin(40), so AE=1unit * sin80/sin40
We now know the length of AD and AE, and Angle DAE=20, according to cosine law:www.ddhw.com
DE^2=AD^2+AE^2-2*AD*AE*cos(20)
After we get DE, we can compute x based on sine law
AD/sin (x) = DE/sin(20), so sin(x) = sin(20)*AD/DE, then x can be computed.
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