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. ${60}^{\circ }$
• B. ${72}^{\circ }$
• C. ${16}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

The correct option is B ${72}^{\circ }$

The formula the arc measure is

$arclength=2\pi R$ $\left(\frac{C}{{360}^{\circ }}\right)$

where

C is the central angle of the arc in degrees

R is the radius of the circle

formula of circumference=$2\pi R$

ration in given $1:5$

therefore

$\frac{arclength}{circumference}$=$\frac{2\pi R\frac{C}{{360}^{\circ }}}{2\pi R}$=$\frac{1}{5}$

$C=\frac{{360}^{\circ }}{5}$

$C={72}^{\circ }$

The angle subtended by the arc at the centre is ${72}^{\circ }$