a kite or a dart
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Not a kite: all its angles are less than 180 degrees.
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No.
A quadrilateral with one reflex angle and 2 pairs of adjacent sides equal is called a kite. A kite is a type of quadrilateral with two distinct pairs of adjacent sides that are equal in length. Additionally, a kite has one reflex angle, which is an angle greater than 180 degrees.
There is no specific limitation on any one angle of an inscribed quadrilateral.
90 degrees That is only true for a square. One interior angle of a quadrilateral can be anything from 0 to 360 degrees (excluding the two extreme values).
If you mean the reflex angle is an interior angle of the triangle then no. The sum of the interior angles of a triangle is 180o, which mean all the angles must be less than 180o, but a reflex angle is greater than 180o and so cannot be one of these angles.