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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.

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