1. The problem states that two lines intersect, forming four angles labeled 1, 2, 3, and 4. 2. We are given that $m \angle 1 = 30^\circ$ and asked to find $m \angle 3$. 3. Recall the property of vertical angles: vertical angles are equal. 4. Since $\angle 1$ and $\angle 3$ are vertical angles, we have: $$m \angle 3 = m \angle 1$$ 5. Substitute the given value: $$m \angle 3 = 30^\circ$$ 6. Therefore, the measure of angle 3 is $30^\circ$. Final answer: $30^\circ$