Given m1 = 79, m3 = 27, and m5 = 82, find the measure of the remaining angles

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

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