Question

an angle has a measure of $\frac{3pi}{20}$ radians. what is the measure of the angle in degrees? use the reference sheet provided here. (there is helpful information at the bottom!) reference sheet the number of degrees of arc in a circle is 360. the number of radians of arc in a circle is 2π. the sum of the measures in degrees of the angles of a triangle is 180. 27 27π 54 54π

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 measure in degrees and $R$ is the measure in radians.

Step2: Substitute the given value

Given $R=\frac{3\pi}{20}$, substituting into the formula gives $D=\frac{3\pi}{20}\times\frac{180^{\circ}}{\pi}$.

Step3: Simplify the expression

The $\pi$ terms cancel out, and $\frac{3\times180}{20}= 3\times9 = 27$. So $D = 27^{\circ}$.

Answer:

A. 27