Question

an angle measures \\(\frac{7}{9}\pi\\) radians. what is the degree measure of the angle?
\\(\circ\\) \\(2.44^\circ\\)
\\(\circ\\) \\(140^\circ\\)
\\(\circ\\) \\(280^\circ\\)
\\(\circ\\) \\(439.6^\circ\\)
done

Explanation:

Step1: Recall radian to degree formula

To convert radians to degrees, use the formula: Degree measure = Radian measure × $\frac{180^\circ}{\pi}$.

Step2: Substitute the given radian measure

The given radian measure is $\frac{7}{9}\pi$. Substitute into the formula: Degree measure = $\frac{7}{9}\pi$ × $\frac{180^\circ}{\pi}$.

Step3: Simplify the expression

The $\pi$ terms cancel out. Then, $\frac{7}{9}×180^\circ = 7×20^\circ = 140^\circ$.

Answer:

140° (corresponding to the option with 140°)