The equivalent degree measure of radians is given by \( \frac{\pi^2}{216} \), which represents the angle in terms of π and simplifies the conversion to degrees. This choice is the correct representation of the angle in simplest terms.
To find the equivalent degree measure of radians, we can use the fact that π radians is equivalent to 180 degrees. The conversion factor is \(\frac{180°}{π}\). Given an angle in radians, you can multiply it by this conversion factor to obtain the equivalent degree measure.
Let \(x\) be the angle in radians. The equivalent degree measure \(D\) is given by:
\[ D = x \times \frac{180°}{π} \]
For simplifying, we'll find the simplest form of \(D\). Now, let's evaluate the answer choices:
a. \( \frac{900}{6} = 150 \) - Not equivalent to radians.
b. \( 216 \) - Not in terms of π.
c. \( \frac{\pi^2}{216} \) - Correct. It's in terms of π and represents the square of π.
d. \( 150° \) - Not equivalent to radians.
Therefore, the correct answer is c. \( \frac{\pi^2}{216} \).