Question

convert the angle \frac{5\pi}{6} from radians to degrees. degrees add work check answer

Explanation:

Step1: Use the conversion formula

To convert radians to degrees, use the formula \( \text{Degrees}=\text{Radians}\times\frac{180^{\circ}}{\pi}\).
Given \( \text{Radians}=\frac{5\pi}{6}\), then \( \text{Degrees}=\frac{5\pi}{6}\times\frac{180^{\circ}}{\pi}\).

Step2: Simplify the expression

Cancel out the \( \pi\) terms: \( \frac{5\cancel{\pi}}{6}\times\frac{180^{\circ}}{\cancel{\pi}}=\frac{5\times180^{\circ}}{6}\).
Now, calculate \( \frac{5\times180}{6}\). Since \( 180\div6 = 30\), then \( 5\times30=150\).

Answer:

\(150\)