At what angle is the arc length half the perimeter of the circle?

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Accepted Answer

The perimeter (circumference) of a circle is given by 2πr. The arc length corresponding to an angle θ (in degrees) is (θ/360) × 2πr. We want the arc length to be half the perimeter, so:

(θ/360) × 2πr = (1/2) × 2πr

Dividing both sides by 2πr:

θ/360 = 1/2

Multiplying both sides by 360:

θ = 180°

Therefore, the angle at which the arc length is half the perimeter of the circle is 180°.

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