Answer
The angle between the vector $\langle1,\sqrt{3}\rangle$ and the x axis is $\theta=\frac{\pi}{3}$.
Work Step by Step
In order to find the angle between the vector $\langle1,\sqrt{3}\rangle$ and the x axis we can simple imagine a triangle with a base of $1$ and a height of $\sqrt{3}$. As a result we can find $\theta$ with simple trigonometry.
$\tan{\theta}=\frac{\sqrt{3}}{1}=\sqrt{3}\Rightarrow\theta=\arctan{\sqrt{3}}=\frac{\pi}{3}$
