After rotating by $60^{\circ}$ about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?

Given: After rotating by $60^{\circ}$ about a center, a figure looks exactly the same as its original position.

To do: To find the other angle at which will this happen for the figure.

Solution: 

If a figure looks like the original figure at one angle, it will look like the original figure at all multiples of that angle.

Thus, if the figure looks the same as its original position when rotated at an angle of $60^{\circ}$, it will look the same when rotated at an angle of $120^{\circ}$, $180^{\circ}$, $240^{\circ}$, $300^{\circ}$, $360^{\circ}$ as they are multiples of it.

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Updated on: 10-Oct-2022

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