Final answer:
The smallest number of degrees a regular octagon can be rotated about its centre to fit its outline is 45 degrees. This is calculated by dividing the total degrees in a full turn (360) by the number of sides the shape has (8).
Step-by-step explanation:
The question is asking what is the smallest number of degrees through which a regular octagon can be rotated about its center to fit its outline. A regular octagon is a eight-sided figure with equal sides and angles. When you divide a full rotation (360 degrees) by the number of sides (8), you get the minimum rotation needed for the regular octagon to fit its outline which is 45 degrees. Therefore, a regular octagon can be rotated a minimum of 45 degrees about its center to fit exactly into the space it originally occupied.
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