The angle between two lines is given by
$ \tan(\theta) = \big|\frac{m_2-m_1}{1+m_1m_2}\big| $
where $m_1$ and $m_2$ are the slopes of the two lines in question.
What is confusing me is the reverse problem. When we try to find the slope of the lines making an acute angle with a line of given slope, say a line of slope $m_1$ is given to us and we are to find the values of $m_2$ making angle $\theta$, we can deduce the two slope values of the two lines from this very formula. But doesn't this formula calculate two angles for the same pair of lines? In short, I would like to know how to interpret the solutions of the above equation for $m_2$ graphically.