# Find the degree measure of the angle subtended at the

Question:

Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm $\left(\right.$ Use $\left.\pi=\frac{22}{7}\right)$

Solution:

We know that in a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre, then

$\theta=\frac{1}{r}$

Therefore, forr $=100 \mathrm{~cm}, \mathrm{l}=22 \mathrm{~cm}$, we have

$\theta=\frac{22}{100}$ radian $=\frac{180}{\pi} \times \frac{22}{100}$ deg ree $=\frac{180 \times 7 \times 22}{22 \times 100}$ deg ree

$=\frac{126}{10}$ deg ree $=12 \frac{3}{5}$ deg ree $=12^{\circ} 36^{\prime} \quad\left[1^{\circ}=60^{\prime}\right]$

Thus, the required angle is $12^{\circ} 36^{\prime}$.

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