You can use Snell's Law. Note that you need two angles for this - the incoming angle, and the outgoing angle.
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Both can be calculated easily using Snell's Law, which you can find easily online. However to use Snell's law you will need one of the angle of incidence or refraction as well as the refractive index of the media the light ray passes through
It is: 180-interior angle = exterior angle
When the angle is 90 degrees.
It depends on what angle. The main angles of a rectangle are all 90 degrees and knowing that does not help. If however, the angle in question is the angle made by the diagonal with one of the sides, then it is possible to use a basic trigonometric ratio to work out the length. Details will depend on which angle is given.
Some of the devices used to measure angle are Transit, Protractor and Compass.