1. **Problem statement:** Given that lines $m$ and $n$ are parallel, and line $q$ is perpendicular to line $p$, with $m \angle 9 = 40^\circ$, find $m \angle 7$. 2. **Relevant facts and formulas:** - When two lines are parallel, corresponding angles are equal. - If a line is perpendicular to another, the angles formed are $90^\circ$. - Vertical angles are equal. 3. **Step-by-step solution:** - Since $m$ and $n$ are parallel and $p$ is a transversal, angles $9$ and $5$ are corresponding angles, so: $$m \angle 5 = m \angle 9 = 40^\circ$$ - Angles $5$ and $7$ are formed where line $q$ intersects line $n$ and $p$. Since $q$ is perpendicular to $p$, angles $7$ and $5$ are complementary (sum to $90^\circ$): $$m \angle 7 + m \angle 5 = 90^\circ$$ - Substitute $m \angle 5 = 40^\circ$: $$m \angle 7 + 40^\circ = 90^\circ$$ - Solve for $m \angle 7$: $$m \angle 7 = 90^\circ - 40^\circ = 50^\circ$$ 4. **Final answer:** $$m \angle 7 = 50^\circ$$