Answer
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Step 1:: Recall the definition of radian measure.
A radian is the measure of the central angle that intercepts an arc of length equal to the radius of the circle. In other words, if the arc length is equal to the radius, then the angle subtended by that arc at the center is 1 radian.
Step 2:: Understand the relationship between the circumference and the diameter of a circle.
The circumference C of a circle is given by the formula C = πd, where d is the diameter of the circle.
Step 3:: Relate radian measure to the circle's circumference.
In a circle with radius r, the arc length subtended by an angle of 1 radian is equal to the radius itself, i.e., r = 1 * r. Now, if we consider an angle of 2π radians, the arc length will be 2π times the radius, which is equal to the circumference of the circle, C = πd.
Step 4:: Relate 2π radians to 360 degrees.
Since 2π radians correspond to the entire circumference of the circle, and there are 360 degrees in one full circle, it follows that 2π radians is equivalent to 360 degrees.
Final Answer
2π radians equals 360 degrees.
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