
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
475.2k+ views
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.
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.
Recently Updated Pages
What percentage of the area in India is covered by class 10 social science CBSE

The area of a 6m wide road outside a garden in all class 10 maths CBSE

What is the electric flux through a cube of side 1 class 10 physics CBSE

If one root of x2 x k 0 maybe the square of the other class 10 maths CBSE

The radius and height of a cylinder are in the ratio class 10 maths CBSE

An almirah is sold for 5400 Rs after allowing a discount class 10 maths CBSE

Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

How do you graph the function fx 4x class 9 maths CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Difference Between Plant Cell and Animal Cell

What is pollution? How many types of pollution? Define it

What is the color of ferrous sulphate crystals? How does this color change after heating? Name the products formed on strongly heating ferrous sulphate crystals. What type of chemical reaction occurs in this type of change.
