right angle triangles have right angles, but there is no such thing as a right angle kite
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A cyclic kite. A kite is cyclic if it has only two right angles.
The diagonals of a kite cross each other at right angles
No, the angles aren't right angles.
A triangle has no right angles when it is not a right angle triangle as for example as in the case of an equilateral triangle that has 3 equal 60 degree angles.
There are no obtuse angles in a right triangle. A right triangle consists of one right angle and two acute angles.