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in Angles and their Measurement by (34.1k points)
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Find the angle subtended at the centre by the circumference of the circle.

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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.

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