To find the radius of a circle from a central angle of 120 degrees, you need additional information, such as the length of the arc or the area of the sector. If you have the arc length (s), you can use the formula ( r = \frac{s}{\theta} ), where ( \theta ) is in radians (120 degrees is ( \frac{2\pi}{3} ) radians). If you know the area of the sector, you can use ( r = \sqrt{\frac{A}{\frac{1}{2} \theta}} ), where ( A ) is the area and ( \theta ) is in radians. Without extra data, the radius cannot be determined solely from the angle.
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The radius of a circle has no bearing on the angular measure of the arc: the radius can have any positive value.
Construct a circle with a 4.5 radius. The circle's circumference is 360 degrees. So mark out 3 by 120 degrees on the circumference and join them to the centre of the circle which will divide the circle into three equal parts.
360 degrees in a circle 120 degrees = 12mm 360 degrees = 36mm Therefore the circumference of the circle is 36mm.
360 ÷ 3 = 120 degrees Therefore the circle (360 degrees) has been split into 3 parts of 120 degrees each.
3.34 units