which of the following degree measures is equal to 3π radians? (the number of degrees of arc in a circle is…

Explanation:

Step1: Set up the proportion

Let (x) be the degree measure. We know that (\frac{\text{Degrees}}{\text{Radians}}=\frac{360}{2\pi}). So (\frac{x}{3\pi}=\frac{360}{2\pi}).

Step2: Cross - multiply

Cross - multiplying gives (2\pi x = 3\pi\times360).

Step3: Solve for (x)

Divide both sides by (2\pi). (x=\frac{3\times360}{2}). Since (\pi) cancels out ((\frac{\pi}{\pi} = 1)), and (3\times180=540).

Answer:

D. (540^{\circ})