The angle between two lines if their slopes are $-2$  and 3

The formula for finding angle between two lines is

$\tan \alpha =\left|\frac{m_2-m_1}{1+m_1{m}_2}\right|$

Given that $m_1=-2$ and $m_2=3$

$\tan \alpha =\left|\frac{3-\left(-2\right)}{1+3\left(-2\right)}\right|=\left|\frac{5}{-5}\right|$

$\tan \alpha =-1$

$\alpha ={\tan }^{-1}\left(-1\right)$