How do I enter  on a broken keyboard? As per title: I've a broken keyboard where the &lt; and > keys don't work anymore. Can I insert such symbols with a Option + X  combination?

I would prefer to avoid direct ASCII code numbers, if possible.
macOS doesn't do 'alt-codes', that's a Windows feature.*  

Simplest solution might be to use the Keyboard Viewer, accessible from the Menu Bar once enabled in: System Preferences > Keyboard > Keyboard 

On a UK keyboard they're accessed by pressing  Shift ⇧  



*From comments:
They can be made to work, though I feel they're more effort than really needed ;)
System Preferences > Keyboard > Input Sources > Plus sign > Unicode Hex input. After you choose it, you can do Option then 003C, it'll show the &lt; symbol.