Question : O is the centre of the circle and $\angle AOB = 150°$, and the shaded portion is $x$ part of the circular region, then what will be the value of $x$?
Option 1: $\frac{1}{12}$
Option 2: $\frac{1}{9}$
Option 3: $\frac{1}{6}$
Option 4: $\frac{1}{4}$
Correct Answer: $\frac{1}{6}$
Solution :
Given: O is the centre of the circle and $\angle AOB = 150°$.
We know that the vertically opposite angles are identical.
⇒ $\angle COD=150°$
Now, The angles between the shaded region and the two angles $\angle AOB$ and $\angle COD$ are making a complete circle.
Let each shaded portion make an angle of $y°$ at the centre.
⇒ $150°+y°+150°+ y°=360°$
⇒ $2y+300°=360°$
⇒ $2y=60°$
⇒ The shaded region covers 60° of the complete circle
i.e., $x=\frac{60°}{360°}=\frac{1}{6}$
Hence, the correct answer is $\frac{1}{6}$.
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