1. **Problem statement:** We need to find the angles of a parallelogram given that the angle between two altitudes drawn from the vertex of an obtuse angle is 60°. 2. **Known facts and formulas:** - Let the parallelogram have angles $\theta$ (acute) and $180^\circ - \theta$ (obtuse). - Altitudes from a vertex are perpendicular to the opposite sides. - The angle between two altitudes from the vertex of the obtuse angle is given as 60°. 3. **Step 1: Define the angles and sides** - Let the obtuse angle be $\alpha = 180^\circ - \theta$. - The two adjacent sides form angles $\alpha$ and $\theta$ at the vertex. 4. **Step 2: Express altitudes directions** - Altitude to side adjacent to angle $\alpha$ is perpendicular to that side. - The angle between the two altitudes is 60°. 5. **Step 3: Use vector or angle relations** - The angle between the two sides is $\alpha$. - The altitudes are perpendicular to these sides, so the angle between altitudes is $180^\circ - \alpha$. 6. **Step 4: Set up equation** - Given angle between altitudes = 60°, so $$ 180^\circ - \alpha = 60^\circ $$ - Solve for $\alpha$: $$ \alpha = 180^\circ - 60^\circ = 120^\circ $$ 7. **Step 5: Find the other angle** - Since angles of parallelogram are supplementary: $$ \theta = 180^\circ - \alpha = 180^\circ - 120^\circ = 60^\circ $$ **Final answer:** The angles of the parallelogram are $120^\circ$ and $60^\circ$.