Hello josemalawiDraw the common tangent at T, meeting YZ at A.

Let angle ATZ = , and angle ATY =

angle YTX =

Now AT = AZ (tangents from A to the circle)

angle AZT = (angles in isosceles triangle)

angle XYT = (exterior angle of triangle YTZ)

Angle YXT = angle YTA = (angle in alternate segment)

angle XTY = (angle sum of triangle XYT)

angle XTW = 180 - angle XTY - angle YTZ (angles on a straight line)

= angle YTZ

QED

Grandad