Answer
$45^{\circ}$
Work Step by Step
To obtain the angle $\theta$ between two non-zero vectors $a$ and $b$, we will use the following formula such as:
$ \theta =\cos^{-1} (\dfrac{\overrightarrow{a} \cdot \overrightarrow{ b} }{|a| |b|})$
We have: $\overrightarrow{a} \cdot \overrightarrow{ b}= (4)(2) +(0) (2) =8$
and $|a|=\sqrt {(4)^2+(0)^2}=4 ; |b|=\sqrt {(2)^2+(2)^2}=\sqrt { 8}$
Therefore, $ \theta =\cos^{-1} (\dfrac{8}{4\sqrt 8})= 45^{\circ}$