Answer
$77.5$ degrees
Work Step by Step
The angle between two vectors is determined using the formula
$\theta=\cos^{-1}\left(\frac{a . b}{|a||b|}\right)$.
If the dot product is zero we would immediately know whether the vectors are orthogonal. Thus we must first find the dot product between the two vectors.
That would be $-2\times5+3\times6=8$.
Thus the vectors aren't orthogonal and the angle is $\cos^-1\left(\frac{8}{|a||b|}\right)$.
The magnitude of the first vector is $\sqrt {(-2)^2+6^2}$ or $2\sqrt {10}$ and the second is $\sqrt {5^2+3^2}$ or $ \sqrt {34}$.
Thus the angle is
$\cos^{-1}\left(\frac{8}{2\sqrt{340}}\right)\approx 77.5$ degrees.
