Question

convert the angle $\theta=\frac{14pi}{9}$ radians to degrees. express your answer exactly. $\theta=square^{circ}$

Explanation:

Step1: Recall conversion formula

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

Step2: Substitute the given value

Substitute $\text{Radians}=\frac{14\pi}{9}$ into the formula: $\theta=\frac{14\pi}{9}\times\frac{180^{\circ}}{\pi}$.

Step3: Simplify the expression

The $\pi$ terms cancel out, and $\frac{14}{9}\times180 = 14\times20=280$. So $\theta = 280^{\circ}$.

Answer:

$280$