Question

Find the measure of the central angle with a radius of 18 inches and the area of a sector measuring 162π square inches

Answer 1

1)we calculate the area of the circle
area of a circle=r²π

Data:
radius=18 in

area of this circle=(18 in)²π=324π in².

2)we calculate the measure of the central angle with area equal 162π in².

324π in²----------------------360º
162π in²----------------------  x

x=(162π in² * 360º) / 324π in²=180º

Answer: 180º.