How can we find the angle of rotation of an object?

The angle of rotation may be defined as the minimum angle through which an object is rotated to attain a structure identical to the original one. 

For example, in the figure shown below, when the image of Taj Mahal is rotated through an angle of 90, we don't get the original structure.

Now, when the Taj Mahal is rotated through an angle of 360°, then we will obtain the original figure as:

So, the above figure has rotational symmetry of order 1 and its angle of rotation is 360°.

These concepts would be more clear to you when you take the different kind of shapes and try to rotate them at different angles.

Form 0° to 360°, the number of times the shape represents its original formation, is refer to as the order of the given shape and the corresponding angles at which it looks exactly as the original shape is the angle of rotation of that object..

Again,

When we rotate the wheel through its center at any angle, we obtain the structure identical to the original wheel.

Therefore, we can say that the wheel has a rotational symmetry of infinite order and its rotation at every angle is known as angle of rotation.

Hope you get it!!