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 angle measure.

 

Key Concept Explanation

The formula for the area of a sector of a circle when the central angle  is in degrees is , where  is the area of the sector,  is the central angle, 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

Click "Show Answer" to reveal the answer and analysis