Answer
$188^{o}$
Work Step by Step
Using (3.6),
$\displaystyle \theta=\tan^{-1}(\frac{-20.0}{-140}) =$(calculator)=$8.1^{o}$, which is in q.I.
Since ($-140\hat{i}-20.0\hat{j}$) points to q.III,
$\theta=8.1^{o}+180^{o}=188^{o}$
(counterclockwise from the $+x$ axis)
