\[\boxed{\text{891.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
\[\angle\alpha + \angle\beta + \angle x = 180 - сумма\ \]
\[углов\ треугольника.\]
\[\angle x = 180{^\circ} - (\angle\alpha + \angle\beta) =\]
\[= 180{^\circ} + \left( - (\angle\alpha + \angle\beta) \right)\]
\[+ \left| \begin{matrix} 58{^\circ} \leq \alpha \leq 59{^\circ} \\ 102{^\circ} \leq \beta \leq 103{^\circ} \\ \end{matrix} \right.\ \]
\[\text{\ \ }\overline{160{^\circ} \leq \alpha + \beta \leq 162{^\circ}}\]
\[- 162{^\circ} \leq - (\angle\alpha + \angle\beta) \leq - 160{^\circ}\]
\[180{^\circ} + ( - 162{^\circ}) \leq 180{^\circ} -\]
\[- (\alpha + \beta) \leq 180{^\circ} + ( - 160{^\circ})\]
\[18{^\circ} \leq \angle x \leq 20{^\circ} - третий\ угол\]
\[\ треугольника.\]
\[Ответ:\ 18{^\circ} \leq \angle x \leq 20{^\circ}.\]