Question

virgil is traveling around a circular island. if he travels a 1000 mile course keeping a constant distance of 200 miles from the center of the island, through what angle does he travel?

Answer 1

we know that
circumference of a circle=2*pi*r
for r=200 miles
circumference of a circle=2*pi*200-----> 1256 miles

if 360° (full circle) has a length of------------------> 1256 miles
X°----------------> 1000 miles
x=1000*360/1256------> x=286.62°

the answer is
286.62 degrees