Maybe thee is an elegant way but

X+y+w+z=360°

Given X+y=w+z

Therefore we can sub X+y with w+z

(W+z)+(w+z)=360°

2(W+z)=360°

Divide both sides by 2

W+z=360°/2

W+z=180°

Straight lines are defined as having/being 180 angle