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A protractor can be used to measure an angle. An angle is basically part of a circle. A complete circle is 360 degrees. A right-angle is 90 degrees, half a circle is 180 degrees, and so on.
Degrees are used to measure the arc of a circle. A full circle is 360 degrees, and a half circle 180. so 9 degrees would be 1/40th of a complete circle.
How many degrees does a circle have? 360 degrees.
How can a circle measure 180 degrees? Circles don't have any angles!
As in a unit circle, 30 degrees is Pi/3.