Since it is given that m6 = m7:
1. Given.
m5 and m6 are vertical angles, which makes them have the same measure, so:
2. Vertical angles have same measure.
m7 and m8 also are vertical angles, so:
3. Vertical angles have same measure.
Since we have m5 = m6 = m7 = m8, then m5 = m8. This is called Transitive Property, so:
4. Transitive propery: m5 = m6 = m7 = m8.