A line makes an angle of $60°$ with each of x and y axis, the which it makes with $z$ axis is ( in degrees) 

Let $\alpha$ be the angle which the line makes with $z$-axis, thus the direction cosines of the line are $\cos {60}^{\circ },\cos {60}^{\circ },\cos \alpha$

$\begin{array}{l}\Rightarrow {\cos }^2{60}^{\circ }+{\cos }^2{60}^{\circ }+{\cos }^2\alpha =1\\ \Rightarrow {\cos }^2\alpha =1-1/4-1/4=1/2\end{array}$

$\Rightarrow \cos \alpha =\pm 1/\sqrt{2}$so $\alpha ={45}^{\circ }.$