Which is the degree measure of ( \frac{5\pi}{6} ) radians?

Correct answer: (150^\circ)

Radians and degrees are two ways of measuring the same angle. The basic conversion fact is \(\pi\) radians equal \(180^\circ\), so \(\frac{\pi}{6}\) radians equals \(30^\circ\). The numerator 5 means that this basic sixth-angle is taken five times. This direct relationship is more reliable than trying to estimate the angle from the decimal value of \(\pi\).

Use \(\frac{5\pi}{6}\times\frac{180^\circ}{\pi}\). The \(\pi\) factors cancel, leaving \(\frac{5\times180^\circ}{6}=5\times30^\circ=150^\circ\). Hence option B is correct. The values \(120^\circ\), \(210^\circ\), and \(300^\circ\) correspond to different multiples of \(\pi/6\), not to five such parts.