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Answer:
[tex]x = 72^{\circ}[/tex]
Explanation:
Given
Shape: Regular Pentagon
Required
Determine the minimum value of x
A pentagon has 5 sides and 1 complete rotation of a pentagon about its centre is 360 degrees
i.e.
[tex]1\ Rotation = 360^{\circ}[/tex]
[tex]Sides= 5[/tex]
The angle of rotation (x) is then calculated as:
[tex]x = \frac{1\ Rotation}{Sides}[/tex]
Substitute values for 1 rotation and sides
[tex]x = \frac{360^{\circ}}{5}[/tex]
[tex]x = 72^{\circ}[/tex]
The above is the minimum value of rotation.
As a bonus
Other possible angle of rotation must be in multiples of 72
i.e.
[tex]x = 72, 144, 216, 288,360....[/tex]
This means that when the pentagon is rotated in any of the above angles of rotation, it will be carried onto itself.