Answer:
[tex]\frac{\pi }{10}[/tex]
Step-by-step explanation:
The area (A) of the sector is calculated using the formula
A = area of circle × fraction of circle
let x be the measure of the central angle, then
A = πr² × [tex]\frac{x}{2\pi }[/tex] ← substitute values
5π = π × 10² × [tex]\frac{x}{2\pi }[/tex]
5π = 100π × [tex]\frac{x}{2\pi }[/tex] (cancel 50π and 2π )
5π = 50x ( divide both sides by 50 )
x = [tex]\frac{5\pi }{50}[/tex] = [tex]\frac{\pi }{10}[/tex] ← central angle
