In part A, the angles are Vertical Angles and are, therefore, congruent. This means you set them equal to one another and solve for X.
[tex]3x + 5 = 5x - 57[/tex]
[tex]62 = 2x[/tex]
[tex]31 = x[/tex]
For part B, the angles are supplementary angles which means they equal 180 degrees.
[tex](4x + 150) + (2x) = 180[/tex]
[tex]6x + 150 = 180[/tex]
[tex]6x = 30[/tex]
[tex]x = 5[/tex]