Ans: C
I is true. The interior angle of the regular $n$-sided polygon
I is true. The interior angle of the regular $n$-sided polygon
$\begin{array}{cl}
= & \dfrac{(n-2)\times180^\circ}{n}
\end{array}$
The exterior angle of the polygon
$\begin{array}{cl}
= & \dfrac{360^\circ}{n}
\end{array}$
Hence, we have
$\begin{array}{rcl}
\dfrac{(n-2)\times180^\circ}{n} & = & 4\times \dfrac{360^\circ}{n} \\
n-2 & = & 8 \\
n & = & 10
\end{array}$
II is false. The number of diagonals of the polygon
$\begin{array}{cl}
= & C^{10}_2 – 10 \\
= & 35
\end{array}$
III is true. For any positive integer $n$, the number of folds of rotational symmetry of $n$-sided polygon is $n$.
