1. **Problem:** If $\angle 1$ and $\angle 2$ are vertical angles and $m\angle 2 = 112^\circ$, find $m\angle 1$. 2. **Formula and rule:** Vertical angles are congruent, meaning they have equal measures. 3. **Apply the rule:** Since $\angle 1$ and $\angle 2$ are vertical angles, $$m\angle 1 = m\angle 2$$ 4. **Substitute the given value:** $$m\angle 1 = 112^\circ$$ 5. **Answer:** $m\angle 1 = 112^\circ$. This means the measure of $\angle 1$ is 112 degrees because vertical angles are always equal.