An angle in standard position has a measure of \frac{5\pi}{6} radians. What is the degree … — ACT

An angle in standard position has a measure of $\frac{5\pi}{6}$ radians. What is the degree measure of this angle?

Answer: 150 degrees

The degree measure of the angle is 150.

To convert an angle from radians to degrees, multiply the radian measure by

\frac{180^\circ}{\pi}

. In this case, multiplying

\frac{5\pi}{6}

\frac{180^\circ}{\pi}

simplifies to

150^\circ

because the

\pi

terms cancel and

180

divided by

6

30

, which is then multiplied by

5

Multiply the given radian measure by the conversion factor

\frac{180^\circ}{\pi}

to convert from radians to degrees.

\frac{5\pi}{6} \times \frac{180^\circ}{\pi}

One full rotation is

360^\circ

, which is equal to

2\pi

radians. Therefore,

180^\circ = \pi

radians, yielding the conversion factor

\frac{180^\circ}{\pi}

Simplify the expression by canceling out common terms.

150^\circ

The common term

\pi

cancels out from the numerator and denominator, leaving

\frac{5 \times 180^\circ}{6} = 5 \times 30^\circ = 150^\circ

Converting radian measures to degree measures

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