Answer
$45 ^ \circ$
Work Step by Step
$2x-y=3$ $\implies$ $a=y=2x-3$ and
$3x+y=7$ $\implies$ $b=y=-3x+7$
Thus, $a= \lt 1,2 \gt$ and $b = \lt 1,-3 \gt$
$ \theta = cos^{-1}\dfrac{a \cdot b}{|a||b|}=cos^{-1}\dfrac{-5}{\sqrt {5}\sqrt {10}}$
$=arccos \frac{-5}{ \sqrt {50}}$
$=arccos \frac{-1}{\sqrt 2}$
$= arccos \frac{-\sqrt 2}{2}$
$=\frac{3 \pi}{4}$
$=135 ^ \circ$
Subtract from $180^ \circ$ to get the acute angle.
$180^ \circ-135 ^ \circ=45 ^ \circ$
