Here's how we get there:
1. Move the first letter to the end: "angel" becomes "ngel"
2. Add "ay" to the end: "ngel" becomes "ngelay"
3. Put the first letter back: "ngelay" becomes "angelway"
Here's how we get there:
1. Move the first letter to the end: "angel" becomes "ngel"
2. Add "ay" to the end: "ngel" becomes "ngelay"
3. Put the first letter back: "ngelay" becomes "angelway"