Answer
(a) $117^{\circ}$ with the x-axis.
(b) $15.9^{\circ}$
(c) $63.4^{\circ}$
Work Step by Step
Throughout, we use the general fact that the angle a vector makes with the x-axis, $\theta$, can be related to its components $A_x$ and $A_y$ as $tan \theta = \frac{A_y}{A_x}$.
Evaluating this ratio for each of the three vectors, we get . . .
for (a): the required angle = $arctan(\frac{-6}{3}) = 117^{\circ}$
for (b): the required angle = $arctan(\frac{2}{7}) = 15.9^{\circ}$
for (c): the required angle = $arctan(\frac{8}{4}) = 63.4^{\circ}$
