using thereoms/postulates, we know that the 60° angle and the (5z - 85)° angle are congruent
so to first find z..
[tex]60 = 5z - 85[/tex]
[tex]145 = 5z[/tex]
[tex]29 = z[/tex]
now that we know z, we can find x
simply replace the z in (5z - 85) with 29
and add the entire angle to x to equal 180
(supplementary angles)
[tex](5(29) - 85) + x = 180[/tex]
[tex](145 - 85) + x = 185[/tex]
[tex]60 + x = 185[/tex]
[tex]x = 125[/tex]
[tex]x = 125 \\ z = 29[/tex]
