The only quadrilaterals with a reflex angle are arrowheads (or chevrons).
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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.
An arrow head
The shape described is a kite, which is a quadrilateral with two pairs of equal adjacent sides and one reflex angle. A kite has an axis of symmetry along the line connecting the midpoints of the non-congruent sides. The reflex angle in a kite is typically greater than 180 degrees, creating a distinct shape that is not a regular quadrilateral.
Kite