My friend... My method wasn't wrong and I couldn't find any mistake on my procedure... Check it out and analyze it by yourself...
Answer:

Step-by-step explanation:
Given
See attachment for circles
Required
Ratio of the outer sector to inner sector
The area of a sector is:
For the inner circle

The sector of the inner circle has the following area

For the whole circle

The sector of the outer sector has the following area

So, the ratio of the outer sector to the inner sector is:


Cancel out common factor

Express as fraction

To solve this problem, you need to use the Phythagorean theorem c^2 is equal to the sum of a^2 and b^2. If a less than or equal to b and b is less than or equal to c or a^2 plus b^2 is greater than c^2 then it is an acute angle.