\(\begin{array}{l}AB\parallel CD \Rightarrow \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over A} \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over C} = \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over B} \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over D} = x\\\\\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over A} \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over B} + \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over B} \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over D} + \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over C} \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over D} + \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over A} \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over C} = 360^\circ \Rightarrow 2x + 160^\circ = 360^\circ \\\\ \Rightarrow 70 + x + 90 + x = 360^\circ \Rightarrow 2x + 160^\circ = 360^\circ \\\\ \Rightarrow 2x = 200^\circ \Rightarrow x = 100^\circ \end{array}\)
1736019749.png)
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