The shape of a decagon will remain the same when it is rotated through
its angle of rotational symmetry.
The rotation about the center will carry a regular decagon back to itself is
36°.
Reasons:
The angle of rotational symmetry of a decagon is the smallest angle that a
decagon can be rotated by such that the image formed by the rotation
coincide with the preimage;
A decagon has 10 sides, the interior angle of a regular decagon is given as
follows;
Each interior angle = [tex]\dfrac{(n - 2) \times 180^{\circ}}{10} = 144^{\circ}[/tex]
A decagon has a reflective symmetry, therefore, the lines of symmetry
joining opposite vertices are straight lines.
The number of diagonals in a decagon = 5
Rotating through the vertex and opposite vertex of the diagonals gives the
number of image of the rotation that is similar to the preimage of a
decagon as ten.
Therefore, a rotation of [tex]\dfrac{360^{\circ}}{10^{\circ}} = 36^{\circ}[/tex], about the center will carry a regular
decagon back to itself.
Learn more here:
https://brainly.com/question/21462859
