The question, "To which of the angels did God ever say...?" appears twice in the chapter, once in verse 5 and again in verse 13, effectively bookending the passage. There are about a half-dozen quotes here; let's categorize them.
|Quotations addressed to...||Quotations simply about...|
So "God sent the angel Gabriel to Nazareth" for example (Luke 1:26). Or we just read, "But the Angel of the Lord called" (Genesis 22:11). True, God did speak directly to Satan (Job 1:7, 2:2-6) but that's not the kind of angel we're talking about here. In any case, the Bible doesn't talk a whole lot about angels, but there is a lot about Messiah, and there's a lot that God says to Messiah too.
Which brings up another point, viz., How does the author of Hebrews know that all these quotations are in fact talking about the Son? That is a huge question, because it underlies not only the book of Hebrews, but a lot of other parts of the New Testament. I'll make the observation for now that to a certain extent, the author of Hebrews reads the Old Testament the way the Lord Jesus Christ read the Old Testament. Consider verse 13, quoting Psalm 110:1. Jesus Christ himself also quotes this verse, identifying the addressee as the Christ (Matthew 22:41-44).
I know that's not an answer, because it just pushes the question one level back (How did Jesus himself identify the addressee as the Christ? Do you have to be God to know what the Old Testament means?) -- but I think it is humanly possible to get a pretty good idea of what these things mean. Not that I have it figured out though! More on this will come in later postings.