Question

Can we have a rotational symmetry of order more than 1 whose angle of rotation is

1. 45°?
2. 17°?

Answer 1

It can be observed that if the angle of rotation of a figure is a factor of 360$$º, then it will have a rotational symmetry of order more than $1$.
It can be checked that $45º$ is a factor of $360º$ but $17º$ is not.
Therefore, the figure having its angle of rotation as $45º$ will have its rotational symmetry of order more than $1$.
However, the figure having its angle of rotation as $17º$ will not be having its rotational symmetry of order more than $1$.