Archangels are exactly as described, responsible for arches of all kinds.
Now this statement may be making you arch your brows, but realize that an archangel is helping you do that. Despite the risk of being called SJWs, archangels are always out there trying to be helpful.
Their most important job is maintaining and supporting bridges that may not be up to snuff anymore. Long ago, an archangel might just stand on a bridge and warn travelers on foot or on horseback that the bridge could be dangerous. Today, with drivers zipping along at 80 mph (130 kph) it is all that they can do to just try and hold a bridge together. Religious fanatics point to bridge collapses as being God's will and punishment for those listening to rock music while on a bridge. But those accidents are due to an archangel being distracted or a bridge being watched over not by an archangel, but by the Angel of Death.
Archangels also aid people suffering from fallen arches. They will visit sufferers and offer to saw off their feet. This will cause them to finally seek treatment. After careful thought, archangels will give 20% off coupons for better quality shoes to those that are found to be worthy.
They are also responsible for making people buy the extremely long running Archie comic books.
As for archvillains and archnemeses, the less said about them and archangels, the better.