答案：(a) $60^\circ$ (b) $36$ (c) $3$
-
$\begin{array}{cl}
& \angle AOB \\
= & 135^\circ – 75^\circ \\
= & 60^\circ
\end{array}$ - 留意 $OA = OB =12$。所以 $\angle OAB = \angle OBA$。由此，可得
$\begin{array}{cl}
& \angle OAB \\
= & \dfrac{1}{2} (180^\circ – \angle AOB) \\
= & \dfrac{1}{2} (180^\circ – 60^\circ) \\
= & 60^\circ
\end{array}$所以，$\angle OAB = \angle OBA = \angle AOB = 60^\circ$。由此，$\Delta OAB$ 為一等邊三角形。所以，$\Delta AOB$ 的周界
$\begin{array}{cl}
= & 3 \times 12 \\
= & 36 \text{ cm}
\end{array}$ - $\Delta AOB$ 的旋轉對稱折數為 $3$。
