**Question:**

A wire of length 121 cm is bent so as to lie along the arc of a circle of radius 180 cm. Find in degrees; the angle subtended at the centre by the arc.

**Solution:**

θ will be in degrees.

Arc-length can be given by the formula : $\theta / 360^{\circ} \times 2 \pi r$

Hence it is given that $121 \mathrm{~cm}$ is the arc length.

$\Rightarrow 121=\theta / 360^{\circ} \times 2 \pi r$

$=121=\theta / 360^{\circ} \times 2 \times 22 / 7 \times 180$

$=121=\theta / 360^{\circ} \times 360 \times 22 / 7$

$=121=\theta \times 22 / 7$

$\Rightarrow \theta=121 \times 7 / 22$

$=38.5^{\circ}$

Hence the angle subtended at the middle is $38.5^{\circ}$

Which can also be written as $38^{\circ} 30 .^{\prime}$