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Question

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.

A
60
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B
72
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C
16
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D
30
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Solution

The correct option is B 72
The formula the arc measure is
arclength=2πR (C360)
where
C is the central angle of the arc in degrees
R is the radius of the circle
formula of circumference=2πR
ration in given 1:5
therefore
arclengthcircumference=2πRC3602πR=15
C=3605
C=72
The angle subtended by the arc at the centre is 72

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