Question

22 multiple choice 1 point find the degree measure of an angle of \frac{2\pi}{5} radians. \frac{\pi}{450}^{\circ} 72\pi^{\circ} 72^{\circ} 1.26^{\circ}

Explanation:

Step1: Recall the conversion formula

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

Step2: Substitute the given value

Given \( \text{Radians}=\frac{2\pi}{5}\), then \( \text{Degrees}=\frac{2\pi}{5}\times\frac{180^{\circ}}{\pi}\).

Step3: Simplify the expression

Cancel out \( \pi\), we get \( \frac{2}{5}\times180^{\circ}\).
\( \frac{2\times180^{\circ}}{5}= 72^{\circ}\).

Answer:

\(72^{\circ}\) (the third option)