2018-I-08

答案：$x = 180^\circ – \theta$, $y = 2\theta – 180^\circ$
考慮圓內接四邊形 $ABCD$。

$\begin{array}{rcll}
x + \theta & = & 180^\circ & \text{(圓內接四邊形的對角)} \\
x & = & 180^\circ – \theta
\end{array}$

由於 $AB//ED$，可得

$\begin{array}{rcll}
\angle ADE & = & x & \text{(錯角，$AB//ED$)} \\
\angle ADE & = & 180^\circ – \theta
\end{array}$

考慮圓內接四邊形 $BCD$。

$\begin{array}{rcll}
\angle BED + \theta & = & 180^\circ & \text{(圓內接四邊形的對角)} \\
\angle BED & = & 180^\circ – \theta
\end{array}$

在 $\Delta DEF$ 中，

$\begin{array}{rcll}
y & = & 180^\circ – \angle FED – \angle FDE & \text{($\Delta$ 的內角和)} \\
y & = & 180^\circ – (180^\circ -\theta) – (180^\circ – \theta) \\
y & = & 2\theta – 180^\circ
\end{array}$