Answer:
1. Given.
2. <5 is supplementary to <4.
2. Angles 5 and 4 are consecutive angles, and by the consecutive angles theorem, the two are supplementary.
3. m<4 + m<5 = 180
3. By the definition of supplementary angles, m<4 + m<5 = 180.
4. m<2 = m<4
4. Angles 2 and 4 are corresponding angles, and by the corresponding angles postulate, the two are congruent. By the definition of congruent angles, m<2 = m<4.
5. m<5 + m<2 = 180
5. Substitution property of equality.