Let the equation of lines are

`y_1= m_1x + c_1` and `y_2= m_2x + c_2`

then angle `phi` between lines `L_1` & `L_2` is given by

`tan phi = |(m_1-m_2)/(1+m_1m_2)|`

`text(Proof :)`

By figure

slope of line `L_1 = tan theta_1 = m_1`

slope of line `L_2 = tan theta_2 = m_2`

In triangle `ABC`

or `theta_1=phi+theta_2`

or `phi =theta_1-theta_2`

or `tan phi = (tan theta_2 - tan theta_1)/(1+tan theta_2 . tan theta_1)`

`tan phi =(m_1-m_2)/(1+m_1m_2)`

& other angle of line `L_2= 180^(circ) - phi`

`:. tan (180^(circ)-phi)= - tan phi =(m_1-m_2)/(1+m_1m_2)`

`:. tan phi = -(m_1-m_2)/(1+m_1m_2)`

`=> tan phi =pm(m_1-m_2)/(1+m_1m_2)`

`:.` the acute angle between the lines would be

`=> tan phi = | (m_1-m_2)/(1+m_1m_2)|`