a nonagon is a nine-sided polygon, if a regular nonagon was rotated about its center point, which of the following angels of rotation would not map the figure onto itself

The angles of rotation that would not map the figure onto itself will not be the multiple of 40 and this can be determined by evaluating the possible angle of each rotation.

Given :

To determine angels of rotation that would not map the figure onto itself, first, evaluate the possible angle of each rotation.

To determine the possible angle of each rotation the following calculation can be used:

The possible angle of each rotation is the ratio of the complete rotation to the number of sides.

Each Rotation =

So, the angles of rotation that would not map the figure onto itself will not be the multiple of 40.

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See Explanation

Step-by-step explanation:

Given

Required

Angles of rotation that would not map the shape on itself

Side of a nonagon is:

and a complete rotation is:

To start with, we calculate a possible angle of each rotation:

This is calculated by dividing the complete rotation by number of sides

The question lacks option; so, it's difficult to give a specific answer.

However, I'll give a generalized answer

For the nonagon to map on itself, the angle must be a multiple of the calculated angle of rotation (40)

i.e.

Any angle different from the above listed angles (or any other multiple of 40 not listed above) answers the question.