Ans: (a) $x=40^\circ$ (b) $900$
- Since the probability that the selected student was born in spring is $\dfrac{1}{9}$, we have
$\begin{array}{rcl}
\dfrac{1}{9} & = & \dfrac{x}{360^\circ} \\
x & = & 40^\circ
\end{array}$ - The angle at centre of the sector Winter
$\begin{array}{cl}
= & 360^\circ – 90^\circ – 158^\circ – 40^\circ \\
= & 72^\circ
\end{array}$Hence, the number of students in the school
$\begin{array}{cl}
= & 180 \div \dfrac{72^\circ}{360^\circ} \\
= & 900
\end{array}$
