Question

Compare an angle having a measure of 120° with that of an angle whose measure is 5 pie over 6 radians. Explain your reasoning.

Answer 1

Answer: The answer is "there is a difference of 30°".

Step-by-step explanation:  We are given to compare an angle having a measure of 120° with that of an angle having a measure of $\dfrac{5\pi}{6}$ radians.

Let the two angles be represented as follows:

${\theta}_1=120^\circ,\\\\{\theta}_2=\dfrac{5\pi}{6}.$

We have the following relation between degree and radian:

$\pi=180^\circ.$

Therefore,

${\theta}_2=\dfrac{5\pi}{6}=\dfrac{5}{6}\times 180^\circ=5\times 30^\circ=150^\circ.$

Hence,

${\theta}_2-{\theta}_1=150^\circ-120^\circ=30^\circ\\\\\Rightarrow {\theta}_2={\theta}_1+30^\circ.$

Thus, the difference is 30°.

Answer 2

Answer:

To compare the angles, write them in terms of the same unit of measure.

Convert 120 degrees to 2(pi)/3 radians, or convert 5(pi)/6 radians to 150 degrees

120 degrees is smaller than 5(pi)/6 radians.

Step-by-step explanation: