$\begin{array}{1 1}(A)\;12^{\large\circ}&(B)\;12^{\large\circ}36'\\(C)\;13^{\large\circ}&(D)\;14^{\large\circ}36'\end{array} $

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- $\theta=\large\frac{l}{r}$
- $\theta$=angle subtended by arc
- $l$=length of the arc
- $r$=radius of the circle
- 1 radian=$(\large\frac{180}{\pi})$

Given :$l=22$cm,r=100cm

$\theta=\large\frac{l}{r}$

$\Rightarrow \large\frac{22}{100}$

$\theta=0.22$radians

We know that

1 radian=$(\large\frac{180}{\pi})$

0.22 radian=$0.22\times \large\frac{180^{\large\circ}}{\pi}$

$\Rightarrow 0.22\times \large\frac{180^{\large\circ}}{22/7}$

$\Rightarrow \large\frac{0.22\times 180\times 7}{22}$

$\Rightarrow \large\frac{126}{10}$$=12^{\large\circ}36'$

Thus the degree measures of the angle subtended at the centre of the circle is $12^{\large\circ}36'$

Hence (B) is the correct answer.

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