Question

What is the order of rotational symmetry of a regular pentagon?
(a) 2
(b) 5
(c) 10
(d) 15

Answer 1

Hint: Read and understand the definitions of certain terms like: - Rotational symmetry, centre of rotation, angle of rotational symmetry and order of rotational symmetry. Now, use the theorem that “a regular polygon of n – sides has ‘n’ order of rotational symmetry” to get the answer.

Complete step by step answer:
Here, we have been asked to find the order of rotational symmetry of a symmetry of a regular pentagon. First let us learn about rotational symmetry and some basic terms related to it.
1. Rotational Symmetry: -
It is the property a shape has when it looks the same after some rotation by a partial turn. For example: - an equilateral triangle will look the same after a partial rotation of \[{{120}^{\circ }}\].
2. Centre of rotation: -
The fixed point around which the rotation occurs is called the centre of rotation. For example: - the centre of rotation of a fan is the centre of the fan from which its blade originates.
3. Angle of Rotational Symmetry: -
The angle of rotational symmetry is the smallest angle for which the figure can be rotated to coincide with itself. For example: - the angle of rotation of an equilateral triangle is \[{{120}^{\circ }}\].
4. Order of Rotational Symmetry: -
The order of rotational symmetry of a shape is the number of times it can be rotated around a full circle and still look the same. For example: - an equilateral triangle can be rotated 3 times around a full circle, each time at the angle of \[{{120}^{\circ }}\], so its order of rotation will be 3.
In general, a regular polygon having n – sides have ‘n’ lines of symmetry and their order of rotational symmetry is ‘n’.
Now, let us come to the question. We have to find the order of rotational symmetry of a regular pentagon.
We know that a regular pentagon has 5 sides. Hence, it will have 5 lines of symmetry and its order of rotational symmetry will be 5.

So, the correct answer is “Option b”.

Note: One may note that without knowing the definitions of the terms given in the solution, we will not be able to solve the question. Remember that sometimes we will be asked the angle of rotational symmetry of a shape. In this case we have to divide \[{{360}^{\circ }}\] with the obtained order of rotational symmetry to get the answer.