The figure shows a quadrilateral \(ABCD\). The exterior angles at \(A\), \(B\) and \(C\) are \(142{}^\circ \), \(105{}^\circ \) and \(\mathrm{136}{}^\circ \) respectively. If reflex \(\angle ADC=x{}^\circ \), find the value of \(x\), stating your reasons clearly.

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