Answer
(a) Refer to the image below for the drawing.
(b) $-\dfrac{5}{6}\pi$ radians
(c) Reference angle = $30^o$ or $\dfrac{\pi}{6}$ radians
Work Step by Step
(a) From the positive x-axis, move 150 degrees clockwise. (refer to the attached image above for the drawing)
(b) Convert to radians by multiplying $\dfrac{\pi}{180^o}$ to obtain:
$-150^o \cdot \dfrac{\pi}{180^o} = -\dfrac{5}{6}\pi$ radians
(c) The angle is in Quadrant III. The reference angle of an angle $\theta$ in Quadrant III is equal to the acute angle that the terminal side makes with the negative x-axis.
Thus, the reference angle of the given angle is:
$\color{blue}{30^o}=30^o \cdot \dfrac{\pi}{180^o}=\color{blue}{\dfrac{\pi}{6}}$ radians.
