Multiple choice

If the arc length and the circumference of a circle are in the ratio $1 : 5$, find the angle subtended by the arc at the centre.

  1. $60^{\circ}$
  2. $72^{\circ}$
  3. $16^{\circ}$
  4. $30^{\circ}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Arc length / Circumference = θ / 360. Given ratio 1/5 = θ / 360. θ = 360 / 5 = 72 degrees.

AI explanation

The proportion of the arc length to the total circumference is equal to the proportion of the central angle to 360 degrees. Setting up the proportion 1/5 equals theta/360 and solving for theta yields 72 degrees.

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