Find the central angle of a sector of a circle if the area of the circle and the area of the sector are in the proportion of 5:3 ( with explanation )

216 degrees

Step-by-step explanation:

The area of a circle = πr^2 while

The area of a sector = θ/360 × πr^2

 if the area of the circle and the area of the sector are in the proportion of 5:3,

Then, area of a circle divided by the area of a sector will be equal to 5/3. That is,

πr^2 ÷ θ/360 × πr^2 = 5/3

πr^2 ÷ θπr^2/360 = 5/3

πr^2 × 360/ θπr^2 = 5/3

πr^2 will cancel out. Leading to

360/θ = 5/3

Cross multiply and make θ the subject of formula

5θ = 3 × 360

θ = 1080/5

θ = 216 degrees

Therefore, the central angle of a sector of a circle is 216 degrees

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