The angels are indeed interested in the actions of humans. The Bible mentions that we are a "theatrical spectacle" to them:
"For it seems to me that God has put us the apostles last on exhibition as men appointed to death, because we have become a theatrical spectacle to the world, and to angels, and to men." (1 Cor. 4:9)
Another aspect in which it is shown that angels take an interest in humans is where the Bible says that the millions of angels rejoice when we come to repentance: “Joy arises among the angels of God over one sinner that repents.” (Luke 15:10) They are very much interested in seeing us maintain faithfulness to the very end and to see mankind reconciled with the heavenly Father, Jehovah.
Also concerning the things that occupied the attention of the Hebrew prophets, the apostle Peter wrote: “Into these very things angels are desiring to peer.” (1 Peter 1:12) Before Jesus Christ came to the earth, the angels were desirous of knowing more about Christ’s sufferings, the “glories to follow these” and the impact of the “good news” on humankind. The apostle Peter could speak of them as “desiring to peer” into these matters. In the original Greek, the expression “to peer” suggests a stooping down with a view to scrutinizing an object more closely.
Since the angels are not all-knowing, they doubtless increase their knowledge by studiously considering God’s dealings and revelations. The arrangement for the redemption of the human race truly furnished a marvelous example of God’s attributes. So by occupying themselves with gaining greater understanding of God’s arrangement for saving sinful mankind, the angels would come to appreciate their heavenly Father even more. They would learn things about his personality and ways that could not be discerned from a study or an examination of any other development in the universe.
For more, see:
The Truth About Angels
Angels - Who are they?
What is an angel?
Angels - Why are they referred to as male in the Bible?
Who were the "sons of God" mentioned in Genesis 6:2?
Do Humans Become Angels When They Die?
Do you have a guardian angel?
Angels - How do they affect us?
Should Christians Expect Divine Protection?
Search For Bible Truths - ARCHIVE
Search For Bible Truths - Search Guide