To convert an angle from radians to degrees, we can use the conversion factor that [tex]\( 180^\circ \)[/tex] is equivalent to [tex]\( \pi \)[/tex] radians. The formula to convert radians to degrees is:
[tex]\[ \text{Degrees} = \text{Radians} \times \left( \frac{180^\circ}{\pi} \right) \][/tex]
We are given an angle of [tex]\( -\frac{2\pi}{5} \)[/tex] radians and need to convert it to degrees. Applying the conversion formula:
[tex]\[ \text{Degrees} = -\frac{2\pi}{5} \times \left( \frac{180^\circ}{\pi} \right) \][/tex]
First, we notice that the [tex]\(\pi\)[/tex] in the numerator and denominator will cancel out:
[tex]\[ \text{Degrees} = -\frac{2 \times 180^\circ}{5} \][/tex]
Next, we multiply the values in the numerator:
[tex]\[ \text{Degrees} = -\frac{360^\circ}{5} \][/tex]
Finally, we perform the division:
[tex]\[ \text{Degrees} = -72^\circ \][/tex]
Therefore, the degree measure of an angle of [tex]\( -\frac{2\pi}{5} \)[/tex] radians is [tex]\( -72^\circ \)[/tex].
