It can have any value at all. A definite value can be determined if the polygon is regular, but there is no justification for assuming that to be the case.
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To calculate the measure of a central angle of a regular nine-sided polygon, divide 360 degrees by the number of sides. In this case, divide 360 by 9. The measure of the central angle of a regular nine-sided polygon is 40 degrees.
Each central angle is (360) divided by (number of sides in the polygon).
Each interior angle of a regular 10 sided decagon measures 144 degrees
the center angle of any polygon is 360 degrees