Angle BOA on the right hand side = w + z = A , let us say
Angle BOA on the left hand side = x + y = A
Both angles are same at O.
Sum = 360 total sum of all angles at any point O
A + A = 360
A = 180 or w+z is 180 deg
Since angle BOA is 180 degrees, it means BO and OA are collinear, that is BOA is a straight line.