Given the measurements of the angles above, the very first angle that we can find is m4. Since angles 3 and 4 are vertical angles, their measures should be the same. So, m4 is also 27. Then by the equation below, we can find the remaining angles,
m1 + m2 + m3 = 180
m4 + m5 + m6 = 180
Substituting the known values,
79 + m2 + 27 = 180 ; m2 = 74
27 + 82 + m6 = 180 ; m6 = 71