1. **State the problem:** Find the angle between the two lines given by the equations $$2x - y = 0$$ and $$3x + y = 0$$. 2. **Rewrite the lines in slope-intercept form:** - For $$2x - y = 0$$, rearranged as $$y = 2x$$, so slope $$m_1 = 2$$. - For $$3x + y = 0$$, rearranged as $$y = -3x$$, so slope $$m_2 = -3$$. 3. **Formula for angle between two lines:** The angle $$\theta$$ between two lines with slopes $$m_1$$ and $$m_2$$ is given by: $$ \tan \theta = \left| \frac{m_1 - m_2}{1 + m_1 m_2} \right| $$ 4. **Calculate $$\tan \theta$$:** $$ \tan \theta = \left| \frac{2 - (-3)}{1 + (2)(-3)} \right| = \left| \frac{5}{1 - 6} \right| = \left| \frac{5}{-5} \right| = 1 $$ 5. **Find $$\theta$$:** Since $$\tan \theta = 1$$, then $$\theta = 45^\circ$$. **Final answer:** The angle between the two lines is $$45^\circ$$.