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Most people will accept the idea of saints (even if they don't agree that their intercession is necessary or helpful) because it seems pretty straightforward to acknowledge that there have been some very holy people over the centuries.
However, angels are a different matter. You can't see angels (in the normal run of events, that is) and so can't prove that they actually exist. Some people get quite twitchy if you mention that you believe in angels: you run the risk of being labelled as a bit soft in the head. After all, aren't angels make-believe, like fairies and elves and pixies... No-one really believes in angels nowadays, do they?
Well, you need to decide whether you believe the Bible. They are mentioned quite a lot... and not just in the early Books of the Old Testament where you might be able to persuade yourself that they're only a representation of some human trait or characteristic or something (that's how I used to "explain" difficult Bible stuff to myself.)
They're awesome creatures... about as unlike popular depictions of fairies and pixies as you can get, and by all accounts they don't resemble those cute little cherubs you see on Christmas cards. As it so happens, the Biblical description of the cherubim is rather hair-raising... and of course, whenever the angels and archangels appear, they seem to tell all and sundry not to be afraid... which rather suggests that their general appearance causes some concern... Those great hulking shepherds in the fields surrounding Bethlehem wouldn't be noted for their timidity, for example... but the appearance of angels had them quaking in their boots.
Roman Miscellany has an excellent post on angels, which you can read HERE (I'd quite forgotten that the Feast used to be called "Michaelmas" !) and Fr. Zuhlsdorf has a close-up of an angel (just an artistic representation, so not at all frightening) embroidered on the beautiful vestments he wore for the Mass he celebrated earlier.
St. Michael, St. Gabriel & St. Raphael, pray for us.