Question

A circle has a radius of length r. If you mark off an arc on the circle of length 2r what is the measurement of the angle that subtends the arc?
A 2pi radians
B. 2 pi r radians
C. 2r radians
D. 2 radians

Answer 1

A full circle has a circumference of 2πr and an angle of 2π radians.

Set up a proportion:
2πr - 2π rad
2r - x rad

$2\pi r \times x = 2\pi \times 2 r \\ 2\pi r x=4 \pi r \\ x=\frac{4 \pi r}{2 \pi r} \\ x=2$

The answer is D. 2 radians.

Answer 2

Answer: 2 radians

Step-by-step explanation: