If r be the radius of the circle, then circumference of the circle = 2πr
Also we know that:
1 radian is the measure of an angle subtended at the centre of a circle of radius r by an arc of length r.
i.e. the angle subtended at the centre by an arc of length r = 1 radian
Angle subtended at the centre by an arc of unit length = \(\frac { 1 }{ r }\) radian
The angle subtended at the centre by an arc of length 2πr
= \(\frac { 1 }{ r }\) x 2πr = 2π radians.
Thus, the angle subtended at the centre of circle by the circumference = 2π.