Circle \(\Gamma\) is the incircle of \(\triangle ABC\) and is also the circumcircle of \(\triangle XYZ\). The point X is on \(\overline{BC}\), the 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 \(\angle YZX\)?
Note that it's YZX, not AYX
