With the information given in the question, the only answer that I can offer is that you measure it, using a protractor.
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It is: 180-interior angle = exterior angle
When the angle is 90 degrees.
Work is minimized when the angle between the force applied and the direction of motion is 90 degrees (or π/2 radians). At this angle, the force does not contribute to the displacement in the direction of the force, resulting in zero work done. In general, as the angle increases from 0 to 90 degrees, the work done decreases, reaching its minimum at 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.
You can use Snell's Law. Note that you need two angles for this - the incoming angle, and the outgoing angle.