This app does what it says on the tin. It measures the angle your phone is at to the nearest degree (no fractions).

Anglemeter has no options at all, perhaps in future the developers could add a couple of embellishments, like the ability to set a reference angle to compare to, or the ability to store a few measured angles.

It is the lack of options that makes this "good" rather than "excellent", but the display is clear, it couldn't be simpler to use, and it looks very nice too.