Why does the angle of descent increase in a constant headwind while decreases in a sudden encounter with a headwind, in a descend?
Consider descending in zero wind, trimmed to an airspeed of 80m/s (288km/h) and a sink rate of 2m/s. You won't touch stick, trim tabs or throttles during the descent, but you will encounter a headwind at a later time. For now, ground speed is equal to airspeed and the angle of descent is 1:40.

You suddenly encounter a headwind of 20m/s. Ground speed remains at 80m/s due to inertia; Airspeed rises to 100m/s. The rise in airspeed increases lift and reduces sink rate to 1m/s. The angle of descent is now much shallower, at 1:80.

After a couple of seconds, airspeed bleeds off and the aircraft resumes its trimmed state at an airspeed of 80m/s and a sink rate of 2m/s. This time, the ground speed is only 60m/s due to the headwind and the angle of descent is now 1:30.