Question

What is the angle of rotation symmetry for a shape that has rotational symmetry of order $5?$
\[\begin{align}
  & A.\ \text{144}{}^\circ \\
 & B.\,36{}^\circ \\
 & C.72{}^\circ \\
 & D.75{}^\circ \\
\end{align}\]

Answer 1

Hint: The given figure or the shape has the rotational symmetry if it can be rotated by any angle between $0{}^\circ $ and $360{}^\circ $ as a result the image coincides with the pre-image.

Complete step-by-step answer:
The angle of the rotational symmetry is the smallest angle for which the given figure can be rotated and coincides with itself. The order of the symmetry is the number of times the figure coincides and rotates through $360{}^\circ $ and the figure looks exactly the same. For example the order of the symmetry of the square is four as it looks the same four times.
To find the angle of rotation symmetry for the shape, we have to divide $360{}^\circ $ by the given order of the rotational symmetry.
Therefore,
$\Rightarrow$ Angle of rotation $=\dfrac{360}{5}$
$\Rightarrow$ Angle of rotation $=72{}^\circ $
Therefore, the required answer - the angle of rotation symmetry for a shape that has rotational symmetry of order $5\text{ is 72}{}^\circ $

Note: Similarly, the order of the given figure can be calculated if the angle fit in is given. Also, instead of the order number, you may be asked with the shape like hexagon, star, triangle, etc. So, remember the symmetry count. For example square has the four line symmetry, triangle has three and both the hexagon and star has five symmetry.