Respuesta :
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 [tex]\dfrac{5\pi}{6}[/tex] radians.
Let the two angles be represented as follows:
[tex]{\theta}_1=120^\circ,\\\\{\theta}_2=\dfrac{5\pi}{6}.[/tex]
We have the following relation between degree and radian:
[tex]\pi=180^\circ.[/tex]
Therefore,
[tex]{\theta}_2=\dfrac{5\pi}{6}=\dfrac{5}{6}\times 180^\circ=5\times 30^\circ=150^\circ.[/tex]
Hence,
[tex]{\theta}_2-{\theta}_1=150^\circ-120^\circ=30^\circ\\\\\Rightarrow {\theta}_2={\theta}_1+30^\circ.[/tex]
Thus, the difference is 30°.
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:
