Notes / Analytic Geometry Angle between two lines Theorem 5.1 of Analytic Geometry · Read in context · PDF Theorem 5.1 (Angle between two lines). Let \(l_1\) and \(l_2\) be non-perpendicular lines with slopes \(m_1\) and \(m_2\), and let \(\alpha \) be the angle from \(l_1\) to \(l_2\) (measured anticlockwise). Then \[ \tan \alpha = \frac {m_2 - m_1}{1 + m_1 m_2}. \]