ANSWER :
The angles are 150 degrees and 210 degrees
EXPLANATION :
Recall the cosine of 30 degrees.
[tex]\cos30=\frac{\sqrt{3}}{2}[/tex]
From the problem, we need to find the measurement of the angle that will give a cosine value of :
[tex]\cos^{-1}(-\frac{\sqrt{3}}{2})[/tex]
Negative values of cosines occur in the Second and Third Quadrant.
Reference angles are always on the x-axis.
Since we know that cos 30 is √3/2, then the value of the angles is 30 degrees.
The first angle must be subtracted from 180 degrees as shown above.
That's 180 - 30 = 150
The second angle must be added to 180 degrees as also shown above.
That's 180 + 30 = 210
