Question 19
Let $XYZ$ be a triangle with $\angle XYZ = 40^{\circ}$ and $\angle YZX = 60^{\circ}$. A circle $\Gamma$, centered at the point $I$, lies inside triangle $XYZ$ and is tangent to all three sides of the triangle. Let $A$ be the point of tangency of $\Gamma$ with $YZ$, and let ray $\overrightarrow{XI}$ intersect side $YZ$ at $B$. Determine the measure of $\angle AIB$.