To convert a given angle from radians to degrees, we use the relationship between radians and degrees. Specifically, we know that:
[tex]\[ 1 \text{ radian} = \frac{180}{\pi} \text{ degrees} \][/tex]
Given the radian measure:
[tex]\[ \frac{5\pi}{6} \text{ radians} \][/tex]
we can convert this to degrees by multiplying by \(\frac{180}{\pi}\).
Step-by-step conversion process is as follows:
1. Write down the original radian measure:
[tex]\[ \frac{5\pi}{6} \][/tex]
2. Multiply this radian measure by \(\frac{180}{\pi}\):
[tex]\[ \left(\frac{5\pi}{6}\right) \times \left(\frac{180}{\pi}\right) \][/tex]
3. Simplify using the property of cancellation:
[tex]\[ \frac{5 \pi \times 180}{6 \pi} \][/tex]
4. The \(\pi\) terms cancel out:
[tex]\[ \frac{5 \times 180}{6} \][/tex]
5. Perform the multiplication and division:
[tex]\[ \frac{900}{6} = 150 \][/tex]
Thus, the equivalent measure in degrees is:
[tex]\[ 150^\circ \][/tex]
Out of the provided options:
- \( 150^\circ \)
- \( 120^\circ \)
- \( 60^\circ \)
- \( 300^\circ \)
The correct answer is:
[tex]\[ 150^\circ \][/tex]
