Measure in degrees and radians of the angle representing 1/3 of a circle is 120 degrees and [tex]\frac{2}{3} \pi[/tex] radians.
What is degree and radian?
Degrees and radians are both ways to write out angle measurements.
A radian is the measure of an angle that, when drawn as a central angle of a circle, intercepts an arc whose length is equal to the length of the radius of the circle.
Degrees are more common in general: there are 360 degrees in a whole circle, 180 degrees in a half circle, and 90 degrees in a quarter of a circle (a right angle).
A circle has a measurement of 360 degrees or 2[tex]\pi[/tex] radians.
Therefore 1/3 of a circle represents the following measures
In degrees
[tex]\frac{1}{3}[/tex] × 360 = 120
In radians
[tex]\frac{1}{3}[/tex] × 2[tex]\pi[/tex]= [tex]\frac{2}{3} \pi[/tex]
Hence, measure in degrees and radians of the angle representing 1/3 of a circle is 120 degrees and [tex]\frac{2}{3} \pi[/tex] radians.
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