In a triangle XYZ, the external angle bisector of angle X and the internal bisector of angle Y meet at W. If angle XZY is 50 degrees, what is angle XWY?

Let the external angle X be 2a. So, angle XWY = a, angle YXZ = 180 - 2a
Let angle XYZ = 2b, so angle XYW = b.
Angle XZY = 180-(180-2a+2b) = 2(a-b) = 50 => a-b = 25
Angle XWY = 180-(180-2a+a+b) = a - b = 25 degrees
Required angle = 25 degrees

Can you explain the Angle XWY = 180-(180-2a+a+b) part?
Shouldn't it be equal to 180-(90-a+b) as external angle bisector of angle X should also bisect the internal angle X?