Final answer:
To compare an angle with a measure of 120° to an angle with a measure of 5π/6 radians, we convert 120° to radians by setting up a proportion. We find that 120° is approximately equal to 2π/3 radians. Thus, both angles represent the same amount of rotation.
Step-by-step explanation:
To compare an angle with a measure of 120° to an angle with a measure of 5π/6 radians, we need to convert one of the measures to the other unit. First, let's convert 120° to radians. There are 2π radians in a full revolution, which is 360°. So, to convert 120° to radians, we can set up the following proportion:
120° / 360° = x radians / 2π radians
Solving for x, we get x ≈ 2π/3 radians.
Now that we have both measures in radians, we can compare them. The angle with a measure of 120° is approximately equal to 2π/3 radians. Both angles represent the same amount of rotation, but may have different arc lengths depending on the distance from the center of rotation.
The key point to remember is that the measure of an angle in radians is directly proportional to its measure in degrees. So, in this case, an angle with a measure of 120° is equal to 2π/3 radians.