Question

The area of a sector is one-twelfth that of the complete circle. Find the angle of the sector.

Answer 1

Area of a sector subtending an angle $\theta$ at the centre is given by $\pi r^2\times \frac{\theta }{{360}^o}$.

As per the question, $\pi r^2\times \frac{\theta }{{360}^o}=\frac{1}{12}\times \pi r^2$

$\Rightarrow \theta =\frac{{360}^o}{12}={30}^o$