Question

A nonagon with a point at the center. the regular nonagon has rotational symmetry of which angle measures? check all that apply. 40° 45° 120° 240° 260° 320°

Answer 1

The degree of rotation for a Nonagon is 40º.

What are the angles in a nonagon?

• Each angle of a regular nonagon is of 140°.
• A nonagon in which all sides are not equal and all angles are not equal.
• The measure of its angles are different but total sum of all its interior angles is always 1260°.

Consider the center of the nonagon. If we join the center to all the vertices, the central angle of 360°, is divided into 9 equal angles, each with a measure of:

360°/9=40°

So to a nonagon rotated 40°, clockwise or counterclockwise, is indistinguishable from the original one.

similarly if we rotate 80 ° c.wise or c.c.wise

in general, a nonagon has a rotational symmetry of 40°n,

where n∈{...-3, -2, -1, 0, 1, 2, 3}...

where 40°n, for n negative, means we are rotating clockwise.

Learn more about regular nonagon

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