There is no set rule establishing the angles on a diamond; even a square (all four corners 90•) turned on edge is a diamond. Generally, a diamond is considered to have two angles less than 90• and two angles greater than 90•, that's it.
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If a diamond does not necessarily have to have right angles in it, but if it does then all four corners have to be right angles. Think of a diamond as a turned square or rhombus.
It simply depends of the length and proportions of the diamond. You have to know the sides of it to determine the angles. ;)
A square must have all four angles equal (at 90o) whereas in a diamond only the opposite angles are equal. A square is a diamond with all four angles right angles.
A geometric diamond has 4 sides and 4 angles. The precious stone has any number of sides and angles - as the cutter determines.
A diamond is also known as a rhombus. A rhombus can have right angles except that it then also becomes a square.