Can a phone without a gyroscope measure angles sufficiently? It seems that a gyroscope sensor is currently not so common amongst Android devices. But does an accelerometer (in conjunction with the compass?) provide enough accuracy to measure angles (tilt, yaw) with high precision?
Sufficiently for what, how high a precision?

There are a number of apps that will measure levels and angles purely using the accelerometer, that are good enough for everyday use, after an initial calibration.

For examples see the range of Spirit Level apps available on the Market.