Question

find the degree measure of an angle of \\( \frac{\pi}{5} \\) radians. \\( \frac{\pi}{900} \\) \\( 0.63 \\) \\( 36 \pi \\) \\( 36 \\) 14 multiple choice 1 point find the radian measure of an angle of \\( -250 \\). \\( \frac{18}{-25 \pi} \\) \\( \frac{-25 \pi}{18} \\) \\( \frac{18 \pi}{-25} \\) \\( \frac{-25}{18 \pi} \\)

Explanation:

Step1: Convert radians to degrees

To convert radians to degrees, use the formula \( \text{Degrees}=\text{Radians}\times\frac{180^{\circ}}{\pi} \).
For \( \frac{\pi}{5} \) radians: \( \frac{\pi}{5}\times\frac{180^{\circ}}{\pi} \).
The \( \pi \) terms cancel out, leaving \( \frac{180^{\circ}}{5}=36^{\circ} \).

Step2: Convert degrees to radians

To convert degrees to radians, use the formula \( \text{Radians}=\text{Degrees}\times\frac{\pi}{180^{\circ}} \).
For \( - 250^{\circ} \): \( -250^{\circ}\times\frac{\pi}{180^{\circ}}=\frac{-25\pi}{18} \).

Answer:

For the first question (converting \( \frac{\pi}{5} \) radians to degrees): \( 36^{\circ} \)
For the second question (converting \( -250^{\circ} \) to radians): \( \frac{-25\pi}{18} \)