For some shapes, there are additional properties in the Transform window (e.g. "Line Properties"). One of these properties is Angle. However, the standard object properties already has an Angle property. How are these different? And what is the relevance of the latter when they conflict? How can they come to be conflicting? For example, here is a line which is clearly horizontal, yet the object angle is 2.5 degrees. Can I reset it to 0?
The two fields are the same value. Change one and the other will update to reflect the same change.
It's merely a duplication in the UI. As for why it's duplicated... you'd have to ask Adobe.
To be honest, I have no clue how you go them to be different values. However, the option to Align to Pixel Grid at the bottom of the Transform panel would suggest you are using an older version of Illustrator. There may have been a bug which was later corrected.