If the angle of rotation is , is it possible to have rotational symmetry of a higher order than 1?

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Yes

In some cases

If angle of rotation is less than

answer is B.

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Detailed Solution

Concept- We must comprehend the definition of rotational symmetry, which is expressed as the maximum number of times a shape may be rotated

and yet retain its original shape. The rotational symmetry order will be represented by that number. After that, we can determine whether or not the provided angle is a factor of

. If so, order will be greater than 1.
Here, it is important to first comprehend what is meant by rotational symmetry.
Rotational symmetry refers to how many times a shape may be rotated in a circle without changing how it appears. Order of rotation is the name given to this number. The original shape of each shape, which is the minimum order, is 1.
To better grasp this, let's use an example.
Question Image

Here, we've used a rectangle whose rotational angle is

. As a result, the first picture is the original picture. Following the

rotation as is evident, the image differs from the actual shape. Then once more following a

rotation the shape is in its original form at

. Similar to how it isn't in its initial form at

and is last at

, it is in its initial shape.
Thus, the

and

versions of the original shape are found here. Thus, rotational symmetry has an order of two.
The rotational symmetry order whose angle is

is what we are now requested to determine. We are aware that

is the result of adding all the angles in any given shape. In this case, the rotational angle will be

. The above example demonstrates how rotation is made up of

, which is a factor of

, or

is not a multiple of

,however. The elements of

can be seen as follows:

2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 45, 60, … …

Not all of the factors can be noted here. The list reveals, however, that 17 is not a factor.
17 cannot divide 360 with a residual of 0 in this case. As a result, there is just one order of rotational symmetry. With a rotational symmetry whose angle is

, we are therefore unable to have rotational symmetry of order greater than 1.
Therefore, option 2 is correct.

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