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If it's 40% of the pie chart, then it takes up 40% of the area of the circle.
It also takes up 40% of the total degrees of the circle.
The total degrees of the circle is 360.
40% of 360 = .4 * 360 = 144 degrees.
The central angle will be 144 degrees.
The area of a circle is equal to pi * r^2
The area of a section of a circle is equal to x/360 * pi * r^2
Since x = 144, then the area of the section of the circle is equal to 144/ 360 * pi * r^2 which is equal to .4 * pi * r^2 which is equal to 40% of the area of the circle.
The simple answer is that 40% of the circle is 40% of the number of degrees in the circumference of the circle which is 40% of 360 which is 144.
If you divide the circle in half, then each half has 180 degrees.
If you divide the circle in fourths, then each fourth has 90 degrees.