Question

Rewrite each degree measure in radians and each radian measure in degrees if the angle is $\frac{5\pi }{6}$.

Short answer

The degree measure of angle $\frac{5\pi }{6}$ is $150°$.

Step-by-step solution

Step 1. Write down the given information.

The given angle in degrees measure is $\frac{5\pi }{6}$.

Step 2. Concept used.

From the degree – radian conversion rule.

$\pi \text{Radian}=180{}^{\circ }....\left(1\right)$

Step 3. Convert degrees measures to radians.

The angle $\frac{5\pi }{6}$ in degrees units is evaluated with the help of concept (1) stated above.

$\begin{array}{l}\frac{5\pi }{6}=\frac{5}{6}\left(\pi \right)\\ =\frac{5}{6}\times \left({180}^{°}\right)\\ ={150}^{°}\end{array}$

Step 4. Conclusion.

The degree measure of angle $\frac{5\pi }{6}$ is $150°$.