Notice that in the image, the angle labeled 6 x + 49 is opposed to the vertex to angle "Z" that means that both must have the SAME measure.
On the other hand, you have two angles that added give 180 degrees (a staright line).
These angles are: (6 x + 49) and (13 x + 55)
SInce they are supplementary angles, they should add up to 180 degrees, and we write the following equation:
(6 x + 49) + (13 x + 55) = 180
remove parenthesis
6 x + 49 + 13 x + 55 = 180
combine like terms
19 x + 104 = 180
subtract 104 from both sides
19 x = 76
divide both sides by 19 to isolate x
x = 76 / 19
x = 4
Now that we know x, we can ca;culate what angle Z is (remember that we said that angle Z is opposed by the vertex to the 6 x + 49 angle,
so we estimate the value of angle Z with
Z = 6 x + 49 = 6 (4) + 49 = 73 degrees