To find the degree measure equivalent of [tex]\(-\frac{11 \pi}{12}\)[/tex] radians, we need to use the conversion factor between radians and degrees. We know that:
[tex]\[ 1 \text{ radian} = \frac{180^{\circ}}{\pi} \][/tex]
Therefore, to convert [tex]\(-\frac{11 \pi}{12}\)[/tex] radians to degrees, we multiply by [tex]\(\frac{180^{\circ}}{\pi}\)[/tex]:
[tex]\[
-\frac{11 \pi}{12} \text{ radians} \times \frac{180^{\circ}}{\pi} = -\frac{11 \pi \times 180^{\circ}}{12 \pi}
\][/tex]
Here, the [tex]\(\pi\)[/tex] terms cancel out:
[tex]\[
-\frac{11 \times 180^{\circ}}{12}
\][/tex]
We can simplify this further by performing the multiplication and division:
[tex]\[
-\frac{1980^{\circ}}{12} = -165^{\circ}
\][/tex]
Thus, the equivalent degree measure of [tex]\(-\frac{11 \pi}{12}\)[/tex] radians is [tex]\(-165^{\circ}\)[/tex]. So, the correct answer is:
[tex]\[ -165^{\circ} \][/tex]
