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 a = $pi r^{2}$ c = $2pi r$ a = $lw$ a = $\frac{1}{2}bh$ $c^{2}=a^{2}+b^{2}$ the number of degrees of arc in a circle is 360. the number of radians of arc in a circle is 2$pi$. the sum of the measures in degrees of the angles of a triangle is 180. 27 54 27$pi$ 54$pi$

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: $D=\frac{3\pi}{20}\times\frac{180^{\circ}}{\pi}$.

Step3: Simplify the expression

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

Answer:

A. 27