God Visits People
I'm not sure what you imagine when you read that an angel visits someone in Scripture. It seems like every time an angel meets with someone, they are terrified! There is an obvious presence from God with you in this moment. Take a moment to read the first two chapters of Luke. How does Zechariah respond to a message from God? How does Mary respond? What is Luke communicating with this contrast of response? When Jesus comes into the world, who does Luke present as the first people to receive the Good News? What is their response?
I was asked once why God doesn't speak to people the way He used to. I questioned if we listen enough to hear God speak. Stopping long enough to listen is a scary notion. If you take time to actually hear God say something...you have to respond.