Question

Area of sector is one twelfth that of a complete circle.Find the angle of sector

Answer 1

let the angle of sector is x

therefore
$\frac{x}{360} \times \pi \times r {}^{2} = \frac{\pi \times r {}^{2} }{12} \\ \\ x = \frac{360}{13} = 30$

Answer 2

Answer:

The angle of the sector if the area of the sector is one-twelfth that of a complete circle = 30

Step-by-step explanation:

Given,

The area of the sector is  $\frac{1}{12}$ th  of the area of a  complete circle

To find,

The angle of the sector

Recall the concepts

Area of the sector = $\frac{\theta}{360}$×πr²

Area of the circle = πr²

Solution

Since the area of the sector is  $\frac{1}{12}$ th  of the area of a  complete circle

$\frac{\theta}{360}$×πr² =  $\frac{1}{12}$πr²

$\frac{\theta}{360}$ =  $\frac{1}{12}$

θ = $\frac{360}{12}$

= 30

The angle of the sector if the area of the sector is one-twelfth that of a complete circle = 30

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