Step-by-step Solution:

We need the angle between the lines \[ 2y = x+1 \quad \Rightarrow \quad y = \tfrac{1}{2}x + \tfrac{1}{2}, \] and \[ y = 3x+2. \] The slopes are \[ m_1 = \tfrac{1}{2}, \quad m_2 = 3. \] The formula for angle \(\theta\) between two lines of slopes \(m_1,m_2\) is \[ \tan\theta = \left| \frac{m_2-m_1}{1+m_1m_2} \right|. \] Substitute: \[ \tan\theta = \left| \frac{3-\tfrac{1}{2}}{1+(3)(\tfrac{1}{2})} \right| = \left| \frac{\tfrac{5}{2}}{1+\tfrac{3}{2}} \right| = \left| \frac{\tfrac{5}{2}}{\tfrac{5}{2}} \right| = 1. \] So \[ \theta = \arctan(1) = 45^\circ. \] Since the problem asks for the **obtuse angle**, we take \[ 180^\circ - 45^\circ = 135^\circ. \] \[ \boxed{135^\circ} \]