Geometry and TrigonometryHardCentral angle from an arc fraction
Geometry and Trigonometry practice question
A circle has circumference 18 centimetres. An arc of the circle has length 6 centimetres. What is the measure, in degrees, of the central angle that subtends the arc?
Answer: 120
The arc is 6/18 = 1/3 of the circle, so the angle is 360/3 = 120°.
Common wrong answers
- If you answered 6
- 6 is the arc length, not an angle.
- If you answered 60
- 60 halves the correct angle (1/6 of the circle would be 3 cm).
- If you answered 108
- 108 uses 6/20 of 360.
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