Find all the angle measures showing all work. which property are you using to set up your equations?

Due to the Property of Opposite Angles, Angle 2 = Angle 4
Therefore: 
x + 16 = 4x - 5                 Add 5 to both sides, subtract x from both sides
21 = 3x 
x = 7 
 
Substituting: 
Angle 2 = 7 +16 = 23°  
Angle 4 = Angle 2 = 23°        Again, Property of Opposite Angles

Due to the Property of Supplementary Angles. Angle 1 + Angle 2 = 180°
23 + Angle 1 = 180
Angle 1 = 157° 

Due to the Property of Opposite Angles, Angle 1 = Angle 3 = 157°