To convert an angle measurement from radians to degrees, we use the conversion factor that [tex]\(180\)[/tex] degrees is equivalent to [tex]\(\pi\)[/tex] radians. Hence, the formula to convert radians to degrees is:
[tex]\[
\text{Degrees} = \text{Radians} \times \left(\frac{180}{\pi}\right)
\][/tex]
Given the angle [tex]\(\theta\)[/tex] in radians:
[tex]\[
\theta = \frac{7\pi}{6}
\][/tex]
We substitute the given value of [tex]\(\theta\)[/tex] into the formula:
[tex]\[
\theta_{\text{degrees}} = \frac{7 \pi}{6} \times \left(\frac{180}{\pi}\right)
\][/tex]
Notice that [tex]\(\pi\)[/tex] in the numerator and denominator cancels out:
[tex]\[
\theta_{\text{degrees}} = \frac{7 \times 180}{6}
\][/tex]
Now, perform the multiplication and division:
[tex]\[
\theta_{\text{degrees}} = \frac{1260}{6}
\][/tex]
Finally, divide [tex]\(1260\)[/tex] by [tex]\(6\)[/tex]:
[tex]\[
\theta_{\text{degrees}} = 210
\][/tex]
Therefore, the equivalent measurement of [tex]\(\theta\)[/tex] in degrees is:
[tex]\[
210
\][/tex]
