Light Outlet Reading 80V
I can't disagree with Paul's response especially when it comes to safety. There are certainly a few things that can be considered here and if you are uncertain I would recommend an electrician because what you describe should never be able to happen and now that is has been identified correcting it is crucial.
Given that you can measure near 120, but it is significantly lower than expected, you almost CERTAINLY have a high resistance connection and this is a recipe for fire. It is possible this is a phantom voltage, but should be treated as live until proven otherwise. Intentionally presume fire is imminent, it could happen at any moment. Now that I got the warning &quot;no kidding this is serious&quot; part out of the way:
Possible likely causes that come to mind:

Aluminum wiring: If your home has aluminum wiring, let us know. There are other posts on this topic that go into details how to resolve this issue short of replacing all wire.
Stab locks/backstabs: these are just... bad. If in the path of your investigation you find these types of connections, fix it. Your future self will thank you.
Bad wire nut connections: this can happen with poor or sloppy twists on wires, or people improperly joining stranded wire with solid wire, loose connections, over-tightening, or just vibrations for a poorly mated connection or a cramped box
Bad Switch, Light Fixture, Outlet, or Breaker: There may be more options here based on what you are running on this circuit, but basically, ANYTHING in the path could be worn out

Steps to resolve:
[Notice: when opening or touching wire, secure power, turn it back on when ready to test]

Identify everything ON THE CIRCUIT shared with this light
If you have an outlet, or other easy access location (be it the switch or the light), test HOT to GROUND, do you get 120V? If so, this means you have a bad Neutral (typically white) return to the box, anywhere in the path (but likely near your light/switch)
If you tested less than (say 114V) from the Hot to Ground, then the issue is on the HOT (typically black); with same location notes as #3
Was there anything else on the circuit from #1? If so, isolate those items, and test the light outlet again, is the voltage higher or lower than the initial 80v? (say +/- 3v) when tested HOT to NEUTRAL
If the voltage on #4 goes up or fluctuates, greater than a few volts, then the issue is most likely upstream and this helps you identify where to check first. Check the items HOT to NEUTRAL moving towards the breaker until (if) you get near a 120v reading. If the voltage stayed near the 80V or you cannot perform a test like #4, then just start from the light fixture and work backwards.

In either case, there is and has been a bad connection in your circuit for possibly a long time. You should check all connections from the light back to the breaker panel. High resistance connections draw more current, thus, more heat. So other connections in the circuit could be, or become, compromised.
Correct any and all bad connections, and replace wiring if sheathing is melted. Contact an electrician if any of this is even remotely questionable.