Solution
Step 1
Theorem
When a transversal crosses two or more parallel lines, vertical opposite angles are equal, alternate interior angles are equal, corresponding angles are equal etc.
Step 2
[tex]\begin{gathered} x\text{ = 130 corresponding angles} \\ x\text{ = 130} \end{gathered}[/tex]
Step 3
[tex]\begin{gathered} y\text{ + 57 = 180 \lparen supplementary angles\rparen} \\ y\text{ = 180 -57} \\ y\text{ = 123} \end{gathered}[/tex]
Step 4
[tex]\begin{gathered} z\text{ + 57 + 50 = 180} \\ z\text{ = 180 - 57 - 50} \\ \text{z = 73} \end{gathered}[/tex]
Final answer
x = 130, y = 123 , z = 73
