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It is: 36/18pi times 360 = about 229 degrees
Whoever wrote this question for you would be happy to see "pi" in the answer rather than "3.14." So I will use pi. Measure of central angle/360=arc length/2pi*r; measure.../360=pi/2pi*9; measure.../360=1/18; measure...=360/18=20. The measure of the central angle is 20 degrees.
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.
arc length/circumference=central angle/360 1/9=central angle/360 central angle=40
If it's a regular 9 sided polygon then each interior angle will measure 140 degrees.