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The number of times that the shape will map back onto itself as the shape rotates 360° about its center is 6.
<h3>What is the sum of all the exterior angles of a regular polygon?</h3>For a regular polygon of any number of sides, the sum of its exterior angle is 360° (full angle).
Regular polygons have all sides the same and that apothem bisects the side in two parts, (provable by symmetry).
A regular polygon with n sides can map onto itself by n times
It will rotate 360°/n about its center every time and will map onto itself
Examples are in the attached table as well as the solution.
The number of times that the shape will map back onto itself as the shape rotates 360° about its center is 6.
Learn more about a regular polygon here:
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