2020-II-19

答案：B
如下圖所示，加入一平行於該兩條平行線的直線。

根據圖像，可得

$\begin{array}{rcll}
w & = & y & \text{(錯角)} \\
u + x & = & 180^\circ & \text{(同旁內角)} \\
x & = & 180^\circ – u
\end{array}$

I 未必正確。若 $u \neq 90^\circ$，則

$\begin{array}{cl}
& u – v + w \\
= & u – (x + y) + w \\
= & u – x – y + w \\
= & u – (180^\circ – u) – w + w \\
= & 2u – 180^\circ \\
\neq & 0 ^\circ
\end{array}$

II 必為正確。

$\begin{array}{cl}
& u + v – w \\
= & u + x + y – w \\
= & u + 180^\circ – u + w – w \\
= & 180^\circ
\end{array}$

III 未必正確。若 $w \neq 135^\circ$，則

$\begin{array}{cl}
& u + v + w \\
= & u + x + y + w \\
= & u + 180^\circ – u + w + w \\
= & 180^\circ + 2w \\
\neq & 450^\circ
\end{array}$