Question

which symbol correctly compares the two angle measures?
\\(\frac{\pi}{4}\\) radians ______ \\(30^\circ\\)
a. <
b. >
c. =

Explanation:

Step1: Convert radians to degrees

To compare the two angle measures, we need to convert \(\frac{\pi}{4}\) radians to degrees. We know that to convert radians to degrees, we use the formula: \( \text{Degrees} = \text{Radians} \times \frac{180^\circ}{\pi} \).

So for \(\frac{\pi}{4}\) radians:

$$ \frac{\pi}{4} \times \frac{180^\circ}{\pi} = \frac{180^\circ}{4} = 45^\circ $$

Step2: Compare the two angle measures

Now we have \(\frac{\pi}{4}\) radians equal to \(45^\circ\) and we need to compare \(45^\circ\) with \(30^\circ\).

Since \(45^\circ > 30^\circ\), we can say that \(\frac{\pi}{4}\) radians \(> 30^\circ\).

Answer:

B. >