1. **State the problem:** We are given two parallel lines $m$ and $n$, and two lines $p$ and $q$ such that $q$ is perpendicular to $p$. We know $m \angle 1 = 30^\circ$ and need to find $m \angle 7$. 2. **Identify relationships:** Since $m$ and $n$ are parallel and $q$ is a transversal, corresponding angles formed by $q$ with $m$ and $n$ are equal. Therefore, $\angle 1$ and $\angle 7$ are corresponding angles. 3. **Use perpendicularity:** Line $q$ is perpendicular to line $p$, so the angles formed at their intersection are $90^\circ$. This confirms the right angle relationships but does not change the equality of corresponding angles. 4. **Apply the corresponding angles theorem:** Since $m \parallel n$ and $q$ is a transversal, corresponding angles are equal: $$m \angle 1 = m \angle 7$$ 5. **Calculate $m \angle 7$:** Given $m \angle 1 = 30^\circ$, then $$m \angle 7 = 30^\circ$$ **Final answer:** $$m \angle 7 = 30^\circ$$