Prove that the angle between the segments from the incenter to two vertices of a triangle has a radian measure equal $\pi/2$ plus one-half the measure of the angle of the triangle at the third vertex

Can someone tell me why we have to show $b = \pi/2 + z/2$? When it says the angle between the segments from the incenter to two vertices... why can't that angle be w? Isn't that also between the segments joining the incenter to the vertices of the triangle?

This may seem like a dumb question, but I am trying to get myself more familiar with reading these geoemtry problems. Please don't solve the problem

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Where are you supposed to have learn this convention...? Should I have learned this in high school? I didn't get that training...(feeling so bad now lol) – Hawk Oct 18 '12 at 4:42
Hard to know how one learns it. Presumably like one learns most conventions: by seeing it often enough implicitly in use. Like in any other natural language, there are many conventions in mathematics, such as typographical conventions, that are rarely explicitly pointed out. – André Nicolas Oct 18 '12 at 4:47

There is a convention that "the" angle between two intersecting non-coincident lines means the angle in the interval $(0,\pi)$.