Geometry

Question Analysis

The main focus is using the formula for the area of a sector to find the central angle. Given the radius and the area of the sector, we need to rearrange the formula to solve for the unknown angle.

 

Key Concept Explanation

The area of a sector of a circle is given by , where is the area of the sector, is the central angle in degrees, and is the radius of the circle. This formula is based on the proportion of the sector's area to the area of the whole circle (), which is related to the proportion of the central angle to .

 

Step - by - Step Solution

1. Start with the sector - area formula .

2. Substitute and into the formula: .

3. First, simplify . The equation becomes

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