You have to combine the gyro and accelerometer (gyro gives angle information, accelerometercorrects for slow drift). The combined angle estimate is then used. [ Caveat - I've programed an IMU, but not actually built a balancing robot! ]
Accelerometers moving in the horizontal plane measure the vector sum of lateral acceleration and g. If the lateral acceleration is zero, g can be used to accurately estimate the tilt angle. Consumer grade accelerometers with much better noise specs that the MPU6050 are available, allowing tilt measurements of better than 1 degree accuracy.
Sure, you can use an accelerometer to measure tilt between 5 and 175 degrees if you are at rest.
Here is one, built into a convenient tool, that measures between 0 and 90 degrees with +/- 0.2 degree accuracy. There are more expensive versions that perform much better.For robotics, I recommend the Bosch BNO055 self contained absolute orientation sensor, which is very easy to use. At least in my hands, it is accurate to about 1 degree in absolute orientation, seemingly regardless of the gyrations it is forced to undergo.