Question

find the degree measure of the angle with the given radian measure.
\frac{31\pi}{18}
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Explanation:

Step1: Recall conversion formula

We know that to convert radians to degrees, we use the formula $D = R\times\frac{180^{\circ}}{\pi}$, where $D$ is the degree - measure and $R$ is the radian - measure.

Step2: Substitute the given value

Given $R=\frac{31\pi}{18}$, substituting into the formula: $D=\frac{31\pi}{18}\times\frac{180^{\circ}}{\pi}$.

Step3: Simplify the expression

The $\pi$ terms cancel out, and $\frac{180}{18}=10$. So $D = 31\times10^{\circ}=310^{\circ}$.

Answer:

$310$