Answer
$74.7 ^ \circ$
Work Step by Step
$x+2y=7$ $\implies$ $a=y=-\frac{1}{2}x+\frac{7}{2}$ and
$5x-y=2$ $\implies$ $b=y=5x-2$
Thus, $a= \lt 2,-1 \gt$ and $b = \lt 1,5 \gt$
$ \theta = cos^{-1}\dfrac{a \cdot b}{|a||b|}=cos^{-1}\dfrac{2(1)+(-1)5}{\sqrt {2^2+(-1)^2}+\sqrt {1^2+5^2}}$
$\approx 105.3 ^ \circ$
Subtract from $180^ \circ$ to get acute angle.
$180^ \circ-105.3 ^ \circ=74.7 ^ \circ$
