, 2024

The angle of one complete rotation measures 360$\degree$. Since the spinner is divided into $5$ equal sections, each $\dfrac{360\degree}{5}=72\degree$ rotation moves the arrow to the next dividing line between two sections. Rotating clockwise, the section labelled $D$ is the $4$th section. This means that if the angle of rotation is greater than $3\times72\degree=216\degree$ and less than$4\times72\degree=288\degree$, then the arrow stops in the section labelled $D$. Since each of the given answers is greater than $360\degree$ and less than $720\degree$, the arrow must have spun through more than one and less than two complete rotations. On the second spin around, the arrow will stop in the section labelled $D$ if the angle of rotation is greater than $216\degree+360\degree=576\degree$ and less than $288\degree+360\degree=648\degree$. Only one of the given answers lies in this range, and so the angle of rotation must be $630\degree$.