\(Circle $\Gamma$ is the incircle of $\triangle ABC$ and is also the circumcircle of $\triangle XYZ$. The point $X$ is on $\overline{BC}$, point $Y$ is on $\overline{AB}$, and the point $Z$ is on $\overline{AC}$. If $\angle A=40^\circ$, $\angle B=60^\circ$, and $\angle C=80^\circ$, what is the measure of $\angle AYX$?\)
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Circle L is the incircle of triangle ABC and is also the circumfrerence of of triangle XYZ. The point X is on line BC, point Y is on line AB, and point Z is on line AC. If angle A = 40 degrees, angle B = 60 degrees, and angle C is 80 degrees, what is the number of degrees of angle AYX.
