Which one of the following angles cannot be constructed using a compass and ruler?

The correct option is D: ${100}^{\circ }$

We can draw ${60}^{\circ }$ and bisect it to get ${30}^{\circ }$.

Similarly, we can bisect ${30}^{\circ }$ and get ${15}^{\circ }$.

Also, we can draw ${90}^{\circ }$ and bisect it to get ${45}^{\circ }$.

But, ${100}^{\circ }$ cannot be drawn using compass and ruler.

Using compass and ruler, we can only draw angles which are multiples of $15$ and also the angles which can be obtained by bisecting it.