#### Answer

$59.5^{ \circ}$

#### Work Step by Step

The the angle between vectors $v$ and $x$-axis is given as:
$ \theta = \cos ^{-1} (\dfrac{v_x}{|v|})$
Here, $v=\lt 3,-5,1 \gt$
$|v|=\sqrt{3^2+(-5)^2+(1)^2}= \sqrt {35}$
Thus, $ \theta = \cos ^{-1} (\dfrac{3}{ \sqrt {35}})=59.5^{ \circ}$