I noticed that I can find the angle between two nodes when I select them, but I wish there was a way to mark the angle on the canvas. Yes, snapping nodes to guides that I duplicate allows me to have consistent angles, but I would like to be able to compare angles between different pairs of nodes, even when I don't have guides present.

Can try using the extension/visualise path/draw handles. 

Also you can convert those drawn handles to guide lines by Shift+G.

Then can drag those guidelines around for comparing or double click them to measure the angle.

Maybe this:

Angle measurements in the measure tool are a bit tricky. During initial drag it will snap the center point but not the side and setting both sides of angle is a bit non obvious. The sequence of steps is something like this:

• click (or click and drag) on the corner, this should snap the corner, doesn't matter where you release the side
• click and drag the red circle, drag it to the one side of angle it should now snap
• once the side has snapped to one of edges press and release ctrl  -> this will update the starting direction from which the angle is measured
• drag the red circle to other side, let it snap