Question

convert the angle $\theta=\frac{23pi}{20}$ 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 $\theta = \frac{23\pi}{20}$ radians. Substituting into the formula, we get $\theta=\frac{23\pi}{20}\times\frac{180^{\circ}}{\pi}$.

Step3: Simplify the expression

The $\pi$ terms cancel out. Then $\frac{23}{20}\times180 = 23\times9=207^{\circ}$.

Answer:

$207$