Can we have a rotational symmetry of order more than 1 whose angle of rotation is:$(i).\ 45^{\circ}$?$(ii).\ 17^{\circ}$?

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Given: Angle of rotation:

$(i).\ 45^{\circ}$?       $(ii).\ 17^{\circ}$?

To do: To find that Can we have rotational symmetry of order more than 1 whose angle of rotation is:

$(i).\ 45^{\circ}$?       $(ii).\ 17^{\circ}$?

Solution:
When an object is rotated in a particular direction, around a point, then it is known as rotational symmetry, also known as radial symmetry. Rotational symmetry exists when a shape is turned, and the shape is identical to the origin.

If the given angle is a factor of $360^{\circ}$, only then the figure will have rotational symmetry of order more than one.

$(i)$. $45^{\circ}$ is a factor of $360^{\circ}$, so the figure will have rotational symmetry of order more than 1 and there would be 8 rotations.

$(ii)$. $17^{\circ}$ is not a factor of $360^{\circ}$, so the figure will not have rotational symmetry of order of more than 1.
Updated on 10-Oct-2022 13:39:21