Answer: 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
