The angle subtended by a diameter is always right. That's Thales' Theorem, one of the first in geometry. We conclude y=90°.
The angle subtended by an arc is half the arc length, so z=50°.
The angles in a triangle add to 180°, so x = 180° - y - z = 40°.
Answer: x=40°, y=90°, z=50°
