find all missing angles in the diagrams below, please help

Answer:
x = 80,
y = 80
Step-by-step explanation:
This is difficult to explain, so here are the theorems used
two lines parallel, with a transversal; alternate interior angles,
verticle angles theorem,
parts - whole postulate,
verticle angles theorem,
parts- whole postulate,
sum angles in a triangle,
supplementary angle, definition straight angle,
parts- whole postulate,
there are many other ways to reach the answer, I just whent this way.
Answer:
x= 80°, y= 100°
Step-by-step explanation:
Please see the attached picture for the full solution.