2014-II-22

$\begin{array}{rcl}
\dfrac{(n-2)\times 180^\circ}{n} & = & \dfrac{360^\circ}{n} + 100^\circ \\
180^\circ n – 360^\circ & = & 360^\circ + 100^\circ n \\
80^\circ n & = & 720^\circ \\
n & = & 9
\end{array}$

II is true. According to the above argument, the polygon is a regular 9-sided polygon. Hence, each exterior angle of the polygon

$\begin{array}{cl}
= & \dfrac{360^\circ}{9} \\
= & 40^\circ
\end{array}$

III is true. The number of axes of reflectional symmetry of a regular 9-sided polygon is $9$.