A regular octagon rotates 360° about its center. How many times does the image of the octagon coincide with the preimage during the rotation?

Answer: 8 timesStep-by-step explanation: By definition, the sum of the exterior angles of a polygon is 360 degrees. Therefore, each exterior angle of the polygon is: [tex]\frac{360\°}{n}[/tex] 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: [tex]=\frac{360\°}{8}=45\°[/tex] 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: [tex]x=\frac{360\°}{45\°}=8\ times[/tex]