For example the current winds aloft forecast for BML shows 155 kts at 30,000 feet:
While 149 kts at the 2,000 ft to 12,000 ft typical of Cessna 172 flight is rare, we had it in Seattle last week (wind speeds on the ground were 20 - 3 kts, at 3,000 feet we had 60 kt winds at 12,000 feet we had 100+ kts, can't remember exactly).
I'd guesstimate in the Seattle area it occurs once every 2 months below 20,000 feet. Above 20,000 feet, it's a regular occurrence.
Flying into 85kt winds will not put you overspeed, flaps down or up (assuming you're airborne, and not on the ground). Wind speed has no effect on aircraft air speed.
If you're flaps-up, engine at 2300 RPM, flying straight-and-level you're going to be cruising around 120kts airspeed in a C172 regardless of a 100kt headwind or 100kt tailwind.
Groundspeed is another story all together (and your fuel consumption getting to your destination).