It is possible, yes.
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That shape would be a trapezoid.
congurent angles are angles that have equal angles. Example, if you want to have equal angles, you have to have a shape that has equal sides
A shape with 4 right angles and 4 equal sides is a square. ==========================
No. They cannot equal 180 degrees unless the kite is square.The kite shape (aka deltoid) is a special case: a bisymmetrical trapezoid with one pair of angles (the sides) equal, and the others not equal (top, bottom). There are two pairs of adjacent equilateral sides.
A shape :) An irregular shape may be a better answer.