In a factory, the distribution of workers across different categories is represented on a pie chart. If category D accounts for exactly $\frac{1}{6}$ th ($16.67\%$) of the total workforce distribution, what is the central angle (angular value) for category D on the pie chart?

1. A
   $30^{\circ }$
2. B
   $60^{\circ }$
3. C
   $90^{\circ }$
4. D
   $80^{\circ }$