The length of JK is 10 units which is also the radius of the circle.
How do we solve for the length of JK?
The measure of angle KJL is 144 degrees and the area of the shaded sector is 40π.
Area of sector = (θ/360)× πr²
The area of the shaded sector is 40π and θ = 144,
40π = (144/360) × πr²
r² = 40π/((144/360) × π)
r² = 40/(2/5)
r² = 100
take the square root of both sides to solve for r:
r = √100 = 10
The radius r, which is the length of , is 10 units