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A kite is a quadrilateral so the sum of its interior angles is 360 degrees.
The top and bottom of a kite will never be equal (unless it is a square)but the left and right angles of the kite will be.
Yes. The opposite angles of a kite can be supplementary if the kite is, more specifically, a square. (90° + 90° = 180°)
Assuming the kite has four sides and is not a square, then yes, it must have obtuse angles.
Congruent means exactly the same in size and angles. Only the two side angles are equal for a kite that is not a square.