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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.
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Solution
Length of the arc = 22 cm
Radius = 100 cm
Now,
\[\theta = \frac{\text{Arc}}{\text{Radius}}\]
\[ = \frac{22}{100}\]
\[ = \frac{11}{50}\text{ radian}\]
∴ Angle subtended at the centre by the arc = \[\left( \frac{11}{50} \times \frac{180}{\pi} \right)^\circ= \left( \frac{11}{5} \times \frac{18}{22} \times 7 \right)^\circ= \left( \frac{63}{5} \right)^\circ= 12^\circ 36'\]
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