Question

for the angle $\frac{5\pi}{6}$, convert it to degree measure. degree measure:

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 radian value

Given \( \text{Radians}=\frac{5\pi}{6}\), substitute into the formula: \( \text{Degrees}=\frac{5\pi}{6}\times\frac{180^{\circ}}{\pi}\).

Step3: Simplify the expression

The \( \pi\) terms cancel out. Then \( \frac{5\times180^{\circ}}{6}\). Calculate \( 180\div6 = 30\), and \( 5\times30^{\circ}=150^{\circ}\).

Answer:

\(150\)