Question

convert the angle $\theta=\frac{8pi}{9}$ radians to degrees. express your answer exactly. $\theta=square^{circ}$

Explanation:

Step1: Recall conversion formula

We know that to convert radians to degrees, we use the formula $\text{Degrees}=\text{Radians}\times\frac{180^{\circ}}{\pi}$.

Step2: Substitute the given value

Given $\theta = \frac{8\pi}{9}$ radians. Substituting into the formula, we get $\theta=\frac{8\pi}{9}\times\frac{180^{\circ}}{\pi}$.

Step3: Simplify the expression

The $\pi$ terms cancel out. $\frac{8}{9}\times180^{\circ}=8\times20^{\circ}=160^{\circ}$.

Answer:

$160$