Every time we have a transversal crossing parallel lines we get eight angles. Each is either congruent or supplementary to any of the other seven, there are only two angle measures in play.
Here we have two transversals, so each has two angle measures. That doesn't count where the two transversals cross; we'll do those last.
On line a we see a 39° angle. Let's do that first.
39°: ∠13 ∠6 ∠5
It's supplement is 180°-39°=141°
141°: ∠14 ∠12 ∠7 ∠4
Line b has a 74° angle
74°: ∠3 ∠15 ∠18
Supplement:
106°: ∠1 ∠2 ∠16 ∠17
OK, now the middle crossing
∠3 + ∠6 + ∠9 = 180°
74° + 39° + ∠9 = 180°
∠9 = 180° - 74° - 39°
∠9 - ∠11 = 67°
∠8 = ∠10 = 180° - 67° = 113°
