Given a circle with r is equal 2cm, can we find the sector's angle?
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Nope...its not possible with the information you have provided.
From common sense and observation you can easily say the value of the central angle is in someway related to the opposite arc length (they are directly proportional).
We know $s=r\theta$ (s=length of arc,r=radius,$\theta$ is the central angle.).(if you want prove ask in comment)
Now,if you have the arc length.You can use this formula to find $\theta$.
Soham
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@user2298766 You can accept the answer by clicking the small green tick mark to acknowledge my answer...thanks!! – Soham Feb 06 '16 at 09:56
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I see. Thanks for your help! – user2298766 Feb 06 '16 at 10:46
