Question: 5. Angles ABC and DEF are complementary angles. If m\angle ABC = 72^\circ, what is m\angle DEF?
1. **State the problem:**
We are given two complementary angles, ABC and DEF, and the measure of angle ABC is $72^\circ$. We need to find the measure of angle DEF.
2. **Recall the definition of complementary angles:**
Two angles are complementary if the sum of their measures is $90^\circ$.
3. **Write the equation:**
$$m\angle ABC + m\angle DEF = 90^\circ$$
4. **Substitute the known value:**
$$72^\circ + m\angle DEF = 90^\circ$$
5. **Solve for $m\angle DEF$:**
$$m\angle DEF = 90^\circ - 72^\circ$$
6. **Calculate:**
$$m\angle DEF = 18^\circ$$
**Final answer:**
The measure of angle DEF is $18^\circ$.