∠1 and ∠2 are supplementary angles, or they equal 180° (supplementary = 180°)
∠1 = x - 19
∠2 = x - 17
Plug in the corresponding expressions with the angles.
(x - 19) + (x- 17) = 180
Combine like terms
x + x = 2x
-19 - 17 = -36
2x - 36 = 180
Isolate the x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
2x - 36 (+36) = 180 (+36)
2x = 180 + 36
2x = 216
Divide 2 from both sides to isolate the x
2x/2 = 216/2
x = 216/2
x = 108
Plug in 108 for x
∠1 = (108) - 19
∠1 = 89°
∠2 = (108) - 17
∠2 = 91°
hope this helps