How could I measure noise of gyroscope angle readings?
You seem to be talking about standard deviation. It is a widely used measure of quality for repetitive measurements, calculated with the following formula: $$\sigma=\sqrt{\frac1 N\Sigma(x_i-\mu)^2} ,\ where\ \mu=\frac1 N\Sigma x_i$$

For a known \$\sigma\$ you can expect 99% of your measurements to be within [+3\$\sigma\$; -3\$\sigma\$] interval. If your application must distinguish between values which are within 3\$\sigma\$ from each other or less, then your measurements are too noisy and you may need a more precise sensor or some sort of noise cancellation algorithm. Otherwise, your measurements are probably fine.

PS. Since your measurements don't give you 90 on average, you probably didn't calibrate your sensor, so you also have an offset error.