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If you mean a toy kite, it could have any number. If you mean the geometrical figure, in Euclidean geometry it could have zero, one, or two. It can't have four because then it would be a square rather than a kite, and it can't have three because that can be proven to be impossible in Euclidean geometry(if it has three, it must of necessity have four thanks to the parallel postulate).

In non-Euclidean geometry (which denies the parallel postulate), a kite with three right angles is possible and is called a Lambert quadrilateral.

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Q: How many right angles dose a kite have?
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