if the lines are parallel
$$ x =z $$ are corresponding angles
$$ z+ y = 180^0 $$ is linear pair
$$ y =55^0 $$ are vertically opposite angles
Substituting the values
$$ z + 55^0 = 180^0 $$
$$ z = 180 -55 = 125^0 $$
IF $$ x =z $$ we get $$ x = 125^0 $$
therefore, $$ x = 125^0 , y =55^0 $$ and $$ z = 125^0 $$