At what angle is the arc length half the perimeter of the circle?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 180°.
Circumference (C) = 2πr
Arc Length (s) = (θ/360°)2πr
The arc length is half the perimeter.
So, s = C/2
⇒ (θ/360°)2πr = (2πr)/2
⇒ θ/360° = 1/2
⇒ θ = 360°/2 = 180°
Therefore, the angle is 180°.