1. **Stating the problem:** We are given two lines and need to find the two possible values of $m$ such that the area of the triangle formed is a certain value (assumed given or to be found). Then, we need to find the acute angle between these two lines. 2. **Formula for area of triangle formed by two lines:** If two lines intersect and form a triangle with the coordinate axes, the area $A$ can be found using the formula: $$A = \frac{1}{2} \times \text{base} \times \text{height}$$ 3. **Finding values of $m$:** Assuming the lines are given in the form $y = mx + c$ or similar, and the triangle is formed with the axes, the intercepts depend on $m$. Using the area formula and given area, set up an equation in $m$. 4. **Solving for $m$:** Solve the quadratic equation obtained from the area condition to find two possible values of $m$. 5. **Finding the acute angle between two lines:** The angle $\theta$ between two lines with slopes $m_1$ and $m_2$ is given by: $$\tan(\theta) = \left| \frac{m_1 - m_2}{1 + m_1 m_2} \right|$$ 6. **Calculate $\theta$:** Use the arctangent function to find $\theta$ in degrees and choose the acute angle (less than 90 degrees). 7. **Final answers:** The two possible values of $m$ are $m_1$ and $m_2$ (from step 4). The acute angle between the lines is $\theta$ degrees (from step 6).