Recall that the dot product between two vectors [tex]\mathbf a[/tex] and [tex]\mathbf b[/tex] satisfies
[tex]\mathbf a\cdot\mathbf b=\|\mathbf a\|\|\mathbf b\|\cos\theta[/tex]
where [tex]\|\mathbf x\|[/tex] denotes the norm of a vector [tex]\mathbf x[/tex], and [tex]\theta[/tex] is the angle between the two vectors.
So if [tex]\mathbf a=(2,3)[/tex] and [tex]\mathbf b=(4,2)[/tex], then
[tex](2,3)\cdot(4,2)=\|(2,3)\|\|(4,2)\|\cos\theta[/tex]
[tex]\implies2\cdot4+3\cdot2=\sqrt{2^2+3^2}\sqrt{4^2+2^2}\cos\theta[/tex]
[tex]\implies\cos\theta=\dfrac{14}{\sqrt{13}\sqrt{20}}[/tex]
[tex]\implies\theta\approx29.7^\circ[/tex]
