The word you are looking for is rotational symmetry and for that an octagon has orders of 8 (that is what you call the times it overlaps) I do not know what you mean on the swcong question
A way of finding out how many orders a shape has of rotational symmetry is by getting some tracing paper and tracing the shape. You then put your pencil on the center of the shape and count how many time the shape overlaps
because the sides of the octagon are all equal so as it rotates from the center it coincides with the preimage
By definition, the sum of the exterior angles of a polygon is 360 degrees.
Therefore, each exterior angle of the polygon is:
Where n is the number of sides of the polygon.
The lengths of the sides of a regular octagon are equal and the measures of the internal angles are equal too.
The sum of the exterior angles of a polygon is 360 degrees and it has 8 sides, therefore, the measure of each exterior angle is:
You know that the regular octagon rotates 360° about its center.
Therefore, keeping all the above on mind, you have that the number of times (which you can call x) the image of the octagon coincide with the preimage during the rotation is:
An octagon has eight sides of equal length and eight angles of same measure. So, If it is rotated 360 degrees about its center. It would coincide with all of its 8 sides. So, it will coincide with it's pre-image 8 times.
because A regular octagon is a closed figure with sides of the same length and internal angles of the same size. so if it is rotated 360 degrees it should coincide with its preimage after every 45 degrees.
so 360/45= 8 times